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## CHARACTERISTIC FUNCTION OF TIME-CHANGED LEVY PROCESSES

We are interested in the question of characteristic function of time-changed Levy process where the random time $T_t$ has a closed form Laplace transform.  Let $Y_t = X_{T_t}$ and $T_t$ is independent of $X_t$.  Then the characteristic function of $Y_t$ is the Laplace transform of $T_t$ evaluated at the characteristic exponent of $X_t$ (timechangeLevy_JFE2004) for Negarive Inverse Gaussian, Variance Gamma, and CGMY models provide examples of this technique (CGMY-SVLevy-2003).

We are interested in random time changes based on Mittag-Leffler distributions, so we consider the Laplace transform formula (Haubold-Mathai-Saxena-MLF2009):

$L[x^{\beta-1} E^\gamma_{\alpha,\beta}(ax^\alpha)] = s^{-\beta}(1-as^{-\alpha})^{-\gamma}$

If we considered time-changed Brownian motion with MLF random times:

$Y(t) = \theta T_t + \sigma W(T_t)$

we set $s= i u \theta + \sigma^2 u^2/2$ into the Laplace transform formula.  In order to calculate the Levy density from the characteristic function, we have to use Sebastian Raible’s Theorem (Corollary 2.4):  Sebastian_Raible

$\frac{d}{ds} \frac{\phi'(s)}{\phi(s)} = \frac{ (2\alpha\beta+\beta)s^\alpha - (\alpha\beta a + \beta a)}{s - a s^{1-\alpha}}$

By Raible’s Theorem, this is the Fourier transform of the measure $|x|^2 K(x) dx$ where $K(x)$ is the Levy density of the time-changed process.

## IN S4 UNIVERSE ALL MASSIVE FERMIONS WILL BE POINT PARTICLES

Consider the exact formula for Dirac eigenspinors on spheres computed by Camporesi-Higuchi (Camporesi-Higuchi-EigenfunctionDiracOnSpheres).  Use the Darboux approximation for Jacobi polynomials.  The major issue is that using the Darboux approximation (see this)and separation of variables, we have the approximation of one of the factors (as $n\rightarrow \infty$)

$\phi_{nl} = \frac{2}{\sqrt{\pi n}} \frac{\cos(Kx+\gamma)}{\sin(x)} + O(n^{-3/2})$

The $\sin(x)$ in the denominator produces a sharp localization.

One can check this directly even for small $n$.

import matplotlib.pyplot as plt
import numpy as np

x=np.linspace(-5e-300,5e-300,1000)
def f(N,l):
a=3./2+float(l)-1
b=3./2+float(l)
gamma=-(a+0.5)*np.pi/2.
K=N+(a+b+1.)/2.
z1=np.sign(np.sin(x))*np.exp(np.log(np.abs(2./np.sin(x)))-0.5*np.log(np.pi*N))
z=z1*np.cos( K*x + gamma)
return(z)

plt.plot(x,f(5,1))
plt.show()

CarrMadan_OptionValuationUsingtheFastFourierTransform_1999

Classical electron radius is $\Delta x =2.82\times 10^{-15} m$ (see this).  Let’s say we are in an $S^4(1/h)$ universe, so in terms of diameter of the universe this is $\Delta x = 1.86 \times 10^{-48} \cdot R_{universe}$.

So we might consider that this corresponds to the $n=10^{48}$-th eigenspinor of the Dirac operator on $S^3(1/h)$, whose eigenvalue is $h n=2.82 \times 10^{-15}$.

If we assume that the Dirac eigenvalues are energy, then we can solve for mass:

$mc^2 = 2.82\times 10^{-15}$

and

$m = 3.13 \times 10^{-32} kg$

The measured mass of electron is $m_e = 9.1\times 10^{-31} kg$, which is off by a factor of 30.

## EIGENSPINORS OF DIRAC OPERATOR ON THREE-SPHERE: WAVE-PARTICLE DUALITY OF FERMIONS

Quantum theory posits some strange features of particles such as ‘wave-particle’ duality.  Here I note that the eigenspinors of the Dirac opertor on a three-sphere have a wavelet-type localization.  In other words, even without a quantum theory, compactness of the space is sufficient to produce localization of Dirac eigenspinors.  From eigenspinors $D_{S^3} \psi_0(x) = \lambda \psi_0(x)$ to the solution of the Dirac wave equation is just multiplication by a phase factor, i.e.

$\psi(t,x) = e^{i\lambda t/\hbar} \psi_0(x)$

solves $D\psi = i\hbar \partial_t \psi$.  With a mass term, one has the Dirac equation

$(mc + D)\psi = i\hbar\partial_t \psi$

Now the eigenspinors have an explicit expression for spheres given by Camporesi-Higuchi.  They find the Dirac eigenspinors by separation of variables for which the first factor can be used to show the ‘wave-particle duality’ issue.  Approximation using the Darboux formula of this factor gives us

$\phi_{nl}(\theta) = 1/\sqrt{n\pi} \cos(N\theta + \gamma)$

where $a=3/2+l-1$

$b=3/2+l$

$N=n+(a+b+1)/2$

$\gamma = -(a+1/2)\pi/2$

Now we can pick a high value say $n=10^{12}$ and look at the graph of $\phi_{n0}(\theta)$ with $\theta \in (-\epsilon_0, \epsilon_0)$.  We can see the localization of the eigenspinor clearly.  Note that no strange theory of wave-particle duality is needed in this case as this is a static eigenspinor of the Dirac operator.  This particular shape of the Dirac eigenspinor is due to the geometry of $S^3$, the global geometry.  I suggest that much of the complex obfuscation of quantum theory would be clarified if one developed physics directly on compact hypersurfaces of a scaled four-sphere which I claim is the actual shape of the universe.  Mystical interpretations of physics arises from this key missing link that we’re in a compact universe.  We need to have a clearer science of physics.  The Big Bang never happened either.  God does not play dice with the universe and so on.

## AN ENIGMA FACED BY DIRAC RESOLVED

Dirac solved the problem of duplexity of point-charge electrons by introducing the matrix square root of the Laplacian operator in 1928.  This was a resolution of experimental problem of observed spectra having twice the expected number of stationary states as the ‘new quantum theory’ following Goudsmit and Uhlenbeck’s introduction of spin angular momentum for the electron.  DiracElectron

Now the Dirac eigenfunctions on $\mathbf{R}^3$ are not compactly supported which makes it harder to interpret the Dirac wavefunctions.  Dirac eigenfunctions on a compact manifold have a better chance of being localized.  On the round three-sphere $S^3$ the eigenspinors can be computed exactly and the localization can be checked directly.  We can make a reasonable conjecture that for perturbations of the great sphere embedded in $S^4(1/h)$ mildly the same localization holds.

## CARR-MADAN 1999, MOODLEY 2005 FOR FFT HESTON/ZULF MODELS

Heston’s original model inverted a characteristic function numerically.  CarrMadan_OptionValuationUsingtheFastFourierTransform_1999 found a way to make FFT practical and Moodley 2005nimalinmoodley2005 provided a Matlab implementation that I adopted to speed up both Heston’s and my time-fractional Heston model.

library(Quandl)
library(plyr)
library(rPython)

library(fOptions)
Quandl.api_key("CoHxdmas1Pz2t7Hk8maE")

timeStart outlier.threshold]thresh){
jumps[k]timeEnd || tau<timeStart){
next
}
S<-surface$underlyingpx[rk] X<-surface$strike[rk]
callPrice<-callHestoncf(surface$underlyingpx[rk], surface$strike[rk],
tau,
rate,
dividendrate,
v0=v0,
vT,
rho,
kappa,
sigma,
implVol=FALSE)
cp<-callPrice[[1]]
#mid0.20){
stars<-'***'
}
#print(sprintf("S=%.2f X=%.2f log(MN)=%.3f tau=%.3f mkt=%.2f heston=%.2f relerr=%.4f abserr=%.3f %s",S,X,log(S/X),tau,mktIV,modelIV,relerr,abserr,stars))
#print(paste('In Heston act mkt iv=',mktIV,' model=',modelIV))

#weight<-exp(-abs(log(S/x)))
weight0.0){
#stimeEnd || tau<timeStart){
next
}

callPrice<-callHestoncf(S,
X,
tau,
rate,
dividendrate,
v0,
vT,
rho,
kappa,
sigma,
implVol=FALSE)
cp<-callPrice[[1]]
#mid0.0){
stars<-''
relerr<-abs(mktIV-modelIV)/mktIV
abserr<-abs(mktIV-modelIV)
abserrors[rk]0.1){
stars<-'***'
}
print(sprintf("S=%.2f X=%.2f log(MN)=%.3f tau=%.3f mkt=%.2f heston=%.2f relerr=%.4f abserr=%.3f %s",S,X,log(S/X),tau,mktIV,modelIV,relerr,abserr,stars))
#print(paste('S=',S,' X=',X,' tau=',tau,' mkt=',mid,' model=',cp,' relerr=',abs(mid-cp)/mid))
}
}
return(abserrors)
}

calibrate.lmheston.model<-function(surface){
ratetimeEnd || tau<timeStart){
next
}
S<-surface$underlyingpx[rk] X<-surface$strike[rk]
#print(c(S,X,tau,rate,dividendrate,v0,vT,rho,kappa,sigma,alpha))

callPrice<-callLMHestoncf(S,
X,
tau,
rate,
dividendrate,
v0,
vT,
rho,
kappa,
sigma,
alpha,
implVol=FALSE)
cp<-callPrice[[1]]
#mid0.20){
stars<-'***'
}

#print(sprintf("S=%.2f X=%.2f log(MN)=%.3f tau=%.3f mkt=%.2f heston=%.2f relerr=%.4f abserr=%.3f %s",S,X,log(S/X),tau,mktIV,modelIV,relerr,abserr,stars))

#weight<-exp(-abs(log(S/X)))
weight0.0){
#stimeEnd || tau<timeStart){
next
}

#callPrice<-lmheston.price(lmheston.params,secparams)
callPrice<-callLMHestoncf(S,
X,
tau,
rate,
dividendrate,
v0,
vT,
rho,
kappa,
sigma,
alpha,
implVol=FALSE)

cp0.0){
stars<-''
relerr<-abs(mktIV-modelIV)/mktIV
abserr<-abs(mktIV-modelIV)
abserrors[rk]0.2){
stars<-'***'
}
print(sprintf("S=%.2f X=%.2f log(MN)=%.3f tau=%.3f mkt=%.2f fracheston=%.2f relerr=%.4f abserr=%.3f %s",S,X,log(S/X),tau,mktIV,modelIV,relerr,abserr,stars))
#print(paste('S=',S,' X=',X,' tau=',tau,' mkt=',mid,' model=',cp,' relerr=',abs(mid-cp)/mid))
}
}
return(abserrors)

}

NDays6){
print(paste('Stock:',symbol))
} else {
return
}

if (1){
lmhparms<-calibrate.lmheston.model(Snew)
#print('Before Heston calibration')
hparms<-calibrate.heston.model(Snew)
#print('Completed Heston calibration')

#print(paste('Completed calibration for',symbol))
}

heston.errors<-compare.heston.versus.market(hparms,Snew)
lmheston.errors<-compare.lmheston.versus.market(lmhparms,Snew)
HestonErr<-append(HestonErr,c(mean(heston.errors)))
LMHestonErr<-append(LMHestonErr,c(mean(lmheston.errors)))
PValues<-append(PValues,t.test(heston.errors,lmheston.errors)$p.value) print(paste(symbol,dates[k],mean(heston.errors),mean(lmheston.errors),sep=",")) } comp<-data.frame(dates[1:length(HestonErr)],HestonErr,LMHestonErr,PValues) colnames(comp)<-c("Date","Heston","fracHeston","PValue") #tt<-t.test(comp$Heston,comp$fracHeston) print(paste(stock,dates[1],dates[NDays],mean(comp$Heston),mean(comp$fracHeston),mean(comp$PValue),sep=","))

compdata.fn<-sprintf("compdata-%s.csv",stock)
write.csv(comp,file=compdata.fn)
#print(comp)
}

files0<-list.files(path="/home/user1/Dropbox/options/bystock/")
files<-sample(files0,1000)
#files<-c("IBM.csv")
for (f in files){
fs<-strsplit(f,"[.]")
stock<-fs[[1]][1]
possibleError<-tryCatch({
heston.vs.lmheston.analysis(stock)
},error=function(e)e)

if (inherits(possibleError,"error")){
next
}
}


## ZULF MODEL FITS LAST TRADE VOLATILITY SURFACE BETTER THAN HESTON MODEL IN MORE THAN 90% IN 56 CASES

 Inbox x

### zulfikar.ahmed@gmail.com<zulfikar.ahmed@gmail.com>

11:09 AM (1 hour ago)

 to jfrenkel, jhansen, jharrington, jharris, jhp, jhricko_4, jhs, jhutasoi, jianjunp, jinha, jjbrehm, jlind, jlondon, jlw, jmateo, jmerseth, jmetcalf, jmg, jmogel, joel, joelms, john.aldrich, john.beatty, johncrawford53, jose.oliveira

I am pleased to announce that our time-fractional Heston model fits the volatility surfaces determined by the LAST TRADE of call options statistically significantly better than the Heston model in 51/55 of the cases (stock/day) that I have checked last night.  The model differs from the Heston model by a single extra parameter 0<alpha<2.  The comparison is to calibrate both the Heston and Zulf models on a volatility surface and record the error of fit (sum of absolute difference of implied volatilities). The paired t-test of these errors give:

>>> ttest_rel(x.ix[:,2],x.ix[:,3])
(array(4.27139160907284), 7.7558339944524236e-05)

Here is the actual table of errors

UPL  2003-01-02  0.0957002682349182  0.0773492111916326
0   UPL  2003-01-03            0.078657        6.652813e-02
1   UPL  2003-01-06            0.069270        5.893240e-02
2   KMI  2002-02-08            0.007780        6.266435e-03
3   KMI  2002-02-11            0.008966        5.994275e-03
4   KMI  2002-02-12            0.008309        5.424351e-03
5   KMI  2002-02-13            0.007713        5.128947e-03
6   KMI  2002-02-14            0.005948        5.272464e-03
7   PAC  2006-11-21            0.000290        1.745138e-07
8   PAC  2006-11-22            0.000558        3.908786e-07
9   NFG  2003-01-02            0.088293        8.326848e-02
10  NFG  2003-01-03            0.092200        1.840495e-02
11  NFG  2003-01-06            0.082446        6.947264e-02
12  NFG  2003-01-07            0.089481        1.946255e-02
13  NFG  2003-01-08            0.091463        8.470383e-02
14  OXY  2002-02-08            0.034763        3.187211e-02
15  OXY  2002-02-11            0.029676        3.690711e-02
16  OXY  2002-02-12            0.022510        1.772629e-02
17  OXY  2002-02-13            0.017657        2.116841e-02
18  OXY  2002-02-14            0.024343        3.202859e-02
19  AEM  2002-02-08            0.123033        1.217102e-01
20  AEM  2002-02-11            0.110734        6.377745e-02
21  AEM  2002-02-12            0.100758        9.943284e-02
22  AEM  2002-02-13            0.088986        8.803400e-02
23  AEM  2002-02-14            0.103508        9.958264e-02
24  NWY  2006-10-11            0.005319        4.450291e-08
25  NWY  2006-10-12            0.001743        1.144806e-07
26  NWY  2006-10-13            0.004078        2.571337e-06
27  NWY  2006-10-16            0.004726        3.099954e-03
28  TEF  2002-02-08            0.010447        5.958070e-03
29  TEF  2002-02-11            0.009764        8.375140e-03
30  CIB  2006-08-18            0.001899        6.670807e-07
31  CIB  2006-08-21            0.001459        8.779171e-09
32  CIB  2006-08-22            0.004307        1.318464e-08
33  CIB  2006-08-23            0.006848        4.271603e-07
34  SKO  2002-02-08            0.059888        4.294716e-02
35  SKO  2002-02-11            0.061167        4.417510e-02
36  SKO  2002-02-12            0.061014        4.901067e-02
37  SKO  2002-02-13            0.055221        4.730380e-02
38  SKO  2002-02-14            0.061628        4.659908e-02
39  PAG  2007-07-03            0.005586        3.715073e-08
40  PAG  2007-07-05            0.008058        1.047600e-06
41  PAG  2007-07-06            0.007521        5.312208e-07
42  PAG  2007-07-09            0.007519        4.822871e-07
43  PAG  2007-07-10            0.006269        7.045978e-07
44  RBK  2002-02-08            0.119141        1.042945e-01
45  RBK  2002-02-11            0.128607        1.035408e-01
46  RBK  2002-02-12            0.131435        1.201102e-01
47  WGO  2002-02-08            0.109837        9.434335e-02
48  WGO  2002-02-11            0.094459        9.186975e-02
49  WGO  2002-02-12            0.109614        8.576695e-02
50  WGO  2002-02-13            0.110616        1.103984e-01
51  WGO  2002-02-14            0.116418        1.109057e-01
52  WAG  2002-02-08            0.059161        6.123514e-02
53  WAG  2002-02-11            0.067877        7.072952e-02
54  WAG  2002-02-12            0.073040        7.199622e-02
55  WAG  2002-02-13            0.060819        5.949971e-02

The situation is very similar to the great breakthrough of Black, Scholes and Merton whose model had a constant volatility assumption which everyone knew was not correct and did not hold in the sense that our alpha parameter is in theory constant per stock but the estimated alpha from last trade volatility surface is not constant.  A possibility that I might explore later is a third stochastic process for alpha but for now we have a clear model that is closed form, almost as fast as Heston model, and that improves the fit of Heston model overwhelmingly often (using last trades and not using bid-ask averages of option prices).
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11:09 AM (1 hour ago)

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Subject: ZULF MODEL FITS LAST TRADE VOLATILITY SURFACE BETTER THAN HESTON
MODEL IN MORE THAN 90% IN 56 CASES
From: “zulfikar.ahmed@gmail.com” <zulfikar.ahmed@gmail.com>
To: jfrenkel@fma.if.usp.br, jhansen@uchicago.edu, jharrington@uchicago.edu,
jharris@andrew.cmu.edu, jhp@uchicago.edu, jhricko_4@juno.com, jhs@math.ubc.ca,
jhutasoi@andrew.cmu.edu, jianjunp@andrew.cmu.edu, jinha@uchicago.edu,
jjbrehm@uchicago.edu, jlind@andrew.cmu.edu, jlondon@uchicago.edu, jlw@jhu.edu,
jmateo@uchicago.edu, jmerseth@uchicago.edu, jmetcalf@ucsc.edu,
jmg@uchicago.edu, jmogel@ucsc.edu, joel@scipp.ucsc.edu, joelms@andrew.cmu.edu,
john.aldrich@vch.ca, john.beatty@interchange.ubc.ca,
johncrawford53@hotmail.com, jose.oliveira@dfn.if.usp.br, josesoto@uem.mz,
jperuma1@jhu.edu, jpino@andrew.cmu.edu, jpitts@uchicago.edu, jpl@stat.cmu.edu,
jpmccorm@uchicago.edu, jr67@andrew.cmu.edu, jrsteinb@illinois.edu,
js5m@andrew.cmu.edu, js6n@andrew.cmu.edu, jsamuels@ucsc.edu,
jthome@andrew.cmu.edu, julia_krause13@hotmail.com, jzal@phas.ubc.ca,
kang@uchicago.edu, karu@math.ubc.ca, kbandura@andrew.cmu.edu,
kboyd@uchicago.edu, kculp@midway.uchicago.edu, kdhah@ucsc.edu,
kebelsduggan@northwestern.edu, keisha@uchicago.edu, keith.miller@bue.edu.eg,
kelbyharrison@northwestern.edu, keshet@math.ubc.ca,
khaled.alshamouty@guc.edu.eg, khan@uchicago.edu, khosravi@math.ubc.ca,
kiefl@triumf.ca, kimberleab@yahoo.com, kiyohara@fge.if.usp.br,
kkoch@andrew.cmu.edu, klein@andrew.cmu.edu, kliu@math.ubc.ca,
km3b@andrew.cmu.edu, kmoriya@andrew.cmu.edu, kmortens@ucsc.edu,
knwoods@cmu.edu, konoplya@fma.if.usp.br, kouslaa@uchicago.edu,
kramanan@andrew.cmu.edu, kramkov@andrew.cmu.edu, ksanders@illinois.edu,
kunalghosh@cmu.edu, kurnikova@cmu.edu, kwarman@andrew.cmu.edu,
kwiat@illinois.edu, kxrobert@ucsc.edu, kzollman@cmu.edu,
l-wedeen@uchicago.edu, lamy@if.usp.br, LauraPapish2010@northwestern.edu,
laurel@andrew.cmu.edu, lberger@andrew.cmu.edu, lburkhdl@interchange.ubc.ca,
lchamon@dfn.if.usp.br, lchristo@andrew.cmu.edu, lesurea@uchicago.edu,
levine@psc.edu, levineweinberg@uchicago.edu, lewis@ucsc.edu,
lfli@andrew.cmu.edu, lievers1@jhu.edu, limauro@andrew.cmu.edu,
lincolnw@andrew.cmu.edu, linda.brown@jhu.edu, liy@andrew.cmu.edu,
llinas@andrew.cmu.edu, lpalmer@andrew.cmu.edu, lskarsga@bccancer.bc.ca,
lsolum@illinois.edu, luxmi@andrew.cmu.edu, lvuocolo@andrew.cmu.edu,
lwright27@jhu.edu, m-mullins@northwestern.edu, m-nayfeh@illinois.edu,
m-silverstein@uchicago.edu, m-stone5@illinois.edu, maclean@math.ubc.ca,
magro@fma.if.usp.br, magyar@math.ubc.ca, maishamiss@gmail.com,
makins@illinois.edu, mandal@andrew.cmu.edu, marchett@if.usp.br,
margolis@interchange.ubc.ca, martha_nussbaum@uchicago.edu, math@math.ubc.ca,
matsuoka@dfn.if.usp.br, mav@physics.ubc.ca, maxcherem2012@northwestern.edu,
maydede@interchange.ubc.ca, mbier@andrew.cmu.edu, mbloom@uchicago.edu,
mblum@cmu.edu, mbspencer@uchicago.edu, mbw@illinois.edu,
mcdawson@uchicago.edu, meierding@uchicago.edu, mestre@illinois.edu,
mfishban@midway.uchicago.edu, mfrise@ucsc.edu, mg0c@andrew.cmu.edu,
mghartlie@hotmail.com, mgomes@fma.if.usp.br, mgp@illinois.edu,
mgray@andrew.cmu.edu, mharrell@cmu.edu, mhassan@bue.edu.eg,
mmuramat@if.usp.br, moborski@andrew.cmu.edu, mohamed.el-rafie@guc.edu.eg,
moore8@andrew.cmu.edu, morris@jhu.edu, mpato@fma.if.usp.br, mriordan@ucsc.edu,
mund@fma.if.usp.br, muthu@uchicago.edu, muwenk@andrew.cmu.edu,
mweems@andrew.cmu.edu, mwilliams@jhu.edu, n-tarcov@uchicago.edu,
nassif@math.ubc.ca, nbaker@andrew.cmu.edu, nelson.carlin@dfn.if.usp.br,
ness@math.ubc.ca, neufeld@pha.jhu.edu, nermeen.serag@guc.edu.eg,
nguyentrh@northwestern.edu, nhassoun@andrew.cmu.edu, njb@math.ubc.ca,
nmisra@andrew.cmu.edu, noelw@andrew.cmu.edu, nsissons@andrew.cmu.edu,
o-maksymchuk@northwestern.edu, ocanter@ucsc.edu, oliveira@if.usp.br,
omar.karam@bue.edu.eg, p-deutscher@northwestern.edu, pallab@phas.ubc.ca,
Paul Roth <paroth@ucsc.edu>, passos@fma.if.usp.br, patrick.leland@jhu.edu,
paujaramillo@if.usp.br, paulini@cmu.edu, pbooke@uchicago.edu,
pcooke1@andrew.cmu.edu, pdelner1@jhu.edu, pdf@pha.jhu.edu, peirce@math.ubc.ca,
pengzhen@andrew.cmu.edu, perkins@math.ubc.ca, peteanu@andrew.cmu.edu,
peter@physics.ucsc.edu, peterjludlow@northwestern.edu, peterson@math.ubc.ca,
petrov@fma.if.usp.br, pgaraud@soe.ucsc.edu, pikhurko@andrew.cmu.edu,
pilchman@ucsc.edu, pisztora@andrew.cmu.edu, piza@fma.if.usp.br,
pjguerns@ucsc.edu, pmarkell@uchicago.edu, profkatz@gmail.com,
profumo@scipp.ucsc.edu, pshekhar@andrew.cmu.edu, pstojan2@jhu.edu,
pvisser@uchicago.edu, randersn@interchange.ubc.ca, rasha.emara@guc.edu.eg,
rballari@interchange.ubc.ca, rbett1@jhu.edu, rblock@andrew.cmu.edu,
rbriere@andrew.cmu.edu, rcarroll@andrew.cmu.edu, rch@pha.jhu.edu,
rclegg@illinois.edu, rcroft@andrew.cmu.edu, rcummins@illinois.edu,
reichst@math.ubc.ca, rf51@cmu.edu, rfroese@math.ubc.ca, rgil@andrew.cmu.edu,
rgleigh@illinois.edu, rgoel@uchicago.edu, rha@ucsc.edu, richer@astro.ubc.ca,
rjasnow@jhu.edu, rjohnson@scipp.ucsc.edu, rk1t@andrew.cmu.edu,
rkelanic@uchicago.edu, rkraut1@northwestern.edu, rm1o@andrew.cmu.edu,
rm5g@andrew.cmu.edu, rmedelstein@gmail.com, robilotta@dfn.if.usp.br,
robtg@ucsc.edu, rolfsen@math.ubc.ca, ronan@jhu.edu, rongchao@andrew.cmu.edu,
rose@phas.ubc.ca, roth99@illinois.edu, rscherba@ucsc.edu, rshd@uchicago.edu,
rstewart@andrew.cmu.edu, russg@illinois.edu, rutesacate@uem.mz,
ruthrichardmoore@comcast.net, rvribas@dfn.if.usp.br, rwestb@jhu.edu,
ryan5@jhu.edu, ryanbdoran@northwestern.edu, s-ebelsduggan@northwestern.edu,
Shelley Anna <sanna@andrew.cmu.edu>, sara@cmu.edu, savitt@interchange.ubc.ca,
sbatiuk1@jhu.edu, sbchavel@uchicago.edu, russ@cmphys.phys.cmu.edu,
sberrym@interchange.ubc.ca, sbevel@uchicago.edu, scheines@cmu.edu,
schneider@cmu.edu, schoetzau@math.ubc.ca, schonbek@ucsc.edu,
schulten@illinois.edu, schumacher@ernest.phys.cmu.edu, scoopbd@gmail.com,
sdasgup2@ucsc.edu, sef@cs.cmu.edu, sej@uchicago.edu, selvin@illinois.edu,
sendsen@cmu.edu, serrede@illinois.edu, sethmayer2014@northwestern.edu,
sev@uchicago.edu, sfenner@uchicago.edu, sfli@andrew.cmu.edu,
sg23@andrew.cmu.edu, sgalloway@uchicago.edu, sgm@uchicago.edu,
sgraul@andrew.cmu.edu, sgross11@jhu.edu, shlomo@andrew.cmu.edu,
David Shwayder <shwayder@illinois.edu>, sieg@cmu.edu, simchen@interchange.ubc.ca,
simons@andrew.cmu.edu, sisotani@fge.if.usp.br, skoplik1@jhu.edu,
slcooper@illinois.edu, james P <strivergreen@gmail.com>, bm@falconfone.com
Content-Type: multipart/mixed; boundary=001a11425f30916b43052ea71c33

—– Message truncated —–

11:09 AM (1 hour ago)

 to me
Delivery to the following recipient failed permanently:

11:09 AM (1 hour ago)

 to me
Delivery to the following recipient failed permanently:

11:09 AM (1 hour ago)

 to me
Delivery to the following recipient failed permanently:

11:09 AM (1 hour ago)

 to me
Delivery to the following recipient failed permanently:

11:09 AM (1 hour ago)

 to me
Delivery to the following recipient failed permanently:

johncrawford53@hotmail.com

Technical details of permanent failure:
Google tried to deliver your message, but it was rejected by the server for the recipient domain hotmail.com by mx3.hotmail.com. [65.55.37.120].

The error that the other server returned was:
550 Requested action not taken: mailbox unavailable

—– Original message —–

DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed;
d=gmail.com; s=20120113;
h=mime-version:date:message-id:subject:from:to;
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SXVg==

11:09 AM (1 hour ago)

 to me
Delivery to the following recipient failed permanently:

o-maksymchuk@northwestern.edu

Technical details of permanent failure:
Google tried to deliver your message, but it was rejected by the server for the recipient domain northwestern.edu by chcspsym3.ads.northwestern.edu. [129.105.238.75].

11:09 AM (1 hour ago)

 to me
Delivery to the following recipient failed permanently:

mghartlie@hotmail.com

Technical details of permanent failure:
Google tried to deliver your message, but it was rejected by the server for the recipient domain hotmail.com by mx3.hotmail.com. [65.55.37.120].

11:09 AM (1 hour ago)

 to me
Delivery to the following recipient failed permanently:

kelbyharrison@northwestern.edu

Technical details of permanent failure:
Google tried to deliver your message, but it was rejected by the server for the recipient domain northwestern.edu by chcspsym3.ads.northwestern.edu. [129.105.238.75].

11:09 AM (1 hour ago)

 to me
Delivery to the following recipient failed permanently:

rmedelstein@gmail.com

Technical details of permanent failure:
Google tried to deliver your message, but it was rejected by the server for the recipient domain gmail.com by gmail-smtp-in.l.google.com. [2607:f8b0:400c:c06::1b].

The error that the other server returned was:
550-5.1.1 The email account that you tried to reach does not exist. Please try
550-5.1.1 double-checking the recipient’s email address for typos or

—– Original message —–

DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed;
d=gmail.com; s=20120113;
h=mime-version:date:message-id:subject:from:to;
bh=5x6aY/1e/aVULsUro7a4B0vTbUG2NcmiHvrStddTlnc=;
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0/3Q==
d=1e100.net; s=20130820;
h=x-gm-message-state:mime-version:date:message-id:subject:from:to;
bh=5x6aY/1e/aVULsUro7a4B0vTbUG2NcmiHvrStddTlnc=;
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rwzA==

11:09 AM (1 hour ago)

 to me
Delivery to the following recipient failed permanently:

ryanbdoran@northwestern.edu

Technical details of permanent failure:
Google tried to deliver your message, but it was rejected by the server for the recipient domain northwestern.edu by chcspsym3.ads.northwestern.edu. [129.105.238.75].

11:09 AM (1 hour ago)

 to me
Delivery to the following recipient failed permanently:

josesoto@uem.mz

Technical details of permanent failure:
Google tried to deliver your message, but it was rejected by the server for the recipient domain uem.mz by webmail.uem.mz. [196.3.96.30].

The error that the other server returned was:
550 5.1.1 <rutesacate@uem.mz>: Recipient address rejected: User unknown in virtual alias table

—– Original message —–

DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed;
d=gmail.com; s=20120113;
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d=1e100.net; s=20130820;
h=x-gm-message-state:mime-version:date:message-id:subject:from:to;
bh=5x6aY/1e/aVULsUro7a4B0vTbUG2NcmiHvrStddTlnc=;
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TuIA==

11:09 AM (1 hour ago)

 to me
Delivery to the following recipient failed permanently:

jpmccorm@uchicago.edu

Technical details of permanent failure:
Google tried to deliver your message, but it was rejected by the server for the recipient domain uchicago.edu by mailgateway03.uchicago.edu. [128.135.107.104].

The error that the other server returned was:
550 5.1.1 <kang@uchicago.edu>… User unknown

—– Original message —–

DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed;
d=gmail.com; s=20120113;
h=mime-version:date:message-id:subject:from:to;
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0/3Q==
d=1e100.net; s=20130820;
h=x-gm-message-state:mime-version:date:message-id:subject:from:to;
bh=5x6aY/1e/aVULsUro7a4B0vTbUG2NcmiHvrStddTlnc=;
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gqdw==

11:09 AM (1 hour ago)

 to me
Delivery to the following recipient failed permanently:

jmetcalf@ucsc.edu

Technical details of permanent failure:
Google tried to deliver your message, but it was rejected by the server for the recipient domain ucsc.edu by aspmx.l.google.com. [2607:f8b0:400c:c0f::1a].

The error that the other server returned was:
550-5.1.1 The email account that you tried to reach does not exist. Please try
550-5.1.1 double-checking the recipient’s email address for typos or

—– Original message —–

DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed;
d=gmail.com; s=20120113;
h=mime-version:date:message-id:subject:from:to;
bh=5x6aY/1e/aVULsUro7a4B0vTbUG2NcmiHvrStddTlnc=;
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0/3Q==
d=1e100.net; s=20130820;
h=x-gm-message-state:mime-version:date:message-id:subject:from:to;
bh=5x6aY/1e/aVULsUro7a4B0vTbUG2NcmiHvrStddTlnc=;
b=m/jHQw+fgVtCXzXT/rP2DePC9zapGmNn016lCKPov739RMlIRG6KNFzpXg7W46FZmj
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UW2g==

11:09 AM (1 hour ago)

 to me
Delivery to the following recipient failed permanently:

11:09 AM (1 hour ago)

 to me
Delivery to the following recipient failed permanently:

11:09 AM (1 hour ago)

 to me
Delivery to the following recipient failed permanently:

rcarroll@andrew.cmu.edu

Technical details of permanent failure:
Google tried to deliver your message, but it was rejected by the server for the recipient domain andrew.cmu.edu by andrew-mx-03.andrew.cmu.edu. [128.2.10.137].

The error that the other server returned was:
553 5.3.0 <mgray@andrew.cmu.edu>… The email account that you tried to reach does not exist.  Please try double-checking the recipient’s email address for typos or unnecessary spaces.

—– Original message —–

DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed;
d=gmail.com; s=20120113;
h=mime-version:date:message-id:subject:from:to;
bh=5x6aY/1e/aVULsUro7a4B0vTbUG2NcmiHvrStddTlnc=;
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0/3Q==
d=1e100.net; s=20130820;
h=x-gm-message-state:mime-version:date:message-id:subject:from:to;
bh=5x6aY/1e/aVULsUro7a4B0vTbUG2NcmiHvrStddTlnc=;
b=fSsXLdguf9EJ5dg8/HKv6oRaTJEu/Vt2NaAXdVFtRaYl98K1qxuuVOj2KGid3fXhJ7
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00XQ==

11:09 AM (1 hour ago)

 to me
Delivery to the following recipient failed permanently:

jmogel@ucsc.edu

Technical details of permanent failure:
Google tried to deliver your message, but it was rejected by the server for the recipient domain ucsc.edu by aspmx.l.google.com. [2607:f8b0:400c:c0f::1a].

11:09 AM (1 hour ago)

 to me
Delivery to the following recipient failed permanently:

11:09 AM (1 hour ago)

 to me
Delivery to the following recipient failed permanently:

mblum@cmu.edu

Technical details of permanent failure:
Google tried to deliver your message, but it was rejected by the server for the recipient domain cmu.edu by cmu-mx-04.andrew.cmu.edu. [128.2.155.69].

The error that the other server returned was:
553 5.3.0 <mblum@cmu.edu>… The email account that you tried to reach does not exist.  Please try double-checking the recipient’s email address for typos or unnecessary spaces.

—– Original message —–

DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed;
d=gmail.com; s=20120113;
h=mime-version:date:message-id:subject:from:to;
bh=5x6aY/1e/aVULsUro7a4B0vTbUG2NcmiHvrStddTlnc=;
b=FGnMb4k3xvj4BOaUhRffFfyq/WX26QOJ2E3P3xtKmMfJ3LjoEJ7iz0Do8NAfjwShu9
4+RS6wwR1qDMAzRau9Wsx6LbPt/JMpHf51/0MbCrfhgEAgPLjDUR+/7nrJCk3R5uDKTi
FjguMbnDh7nkFp03IVgkV/ehTVO4IDU/Cb4vKrSxNfs6n1EPaS9YHH9N+NtSU3m/XObv
NR9/JNO/WP0L4qIPuKk5hxuSycYgo0lKFKg+zyGiauu54hL5b4tCvvDRAIQql/jtG7QT
Jx1i19Gy+XWUBAwQme3t+UjE2WAoksAUuFJk7XCJO2rx5hGhq2ccpRsoOhFA1nZl4fc7
0/3Q==
d=1e100.net; s=20130820;
h=x-gm-message-state:mime-version:date:message-id:subject:from:to;
bh=5x6aY/1e/aVULsUro7a4B0vTbUG2NcmiHvrStddTlnc=;
b=encO0dJykXEX3RMdD4r4vkX8S789jK0H48Ufw5uhF+n7cmox4sKyytBCCemxqHIRSu
c7f9xc8kb9BY7+y19RsvFIpVeGEQ16t5Yri7GUNcCwWgHLUIro7Hc3abcNtmt2xhPfcD
c7YMguiGOuGlCHUfuKxo8f+4VhptOEc3vOPJL/VhYERRJD9/J1gbWPtQ1Gzw0oPalkaJ
9/6NHUiDQzpnV7DODzdl19uz8BTRdZDFgR3OOI83KNMrowY2zfaKQSVvlqLFVV6GzxO9
o9oTo7oatiN+fQmbhjDO1bZcnQZN1ngSYpUbXunWt5gpHGv20wErn4dBk8Z0YI73TwGt
waWQ==

11:09 AM (1 hour ago)

 to me
Delivery to the following recipient failed permanently:

11:09 AM (1 hour ago)

 to me
Delivery to the following recipient failed permanently:

jperuma1@jhu.edu

Technical details of permanent failure:
Google tried to deliver your message, but it was rejected by the server for the recipient domain jhu.edu by smtp.johnshopkins.edu. [162.129.198.15].

The error that the other server returned was:

—– Original message —–

DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed;
d=gmail.com; s=20120113;
h=mime-version:date:message-id:subject:from:to;
bh=5x6aY/1e/aVULsUro7a4B0vTbUG2NcmiHvrStddTlnc=;
b=FGnMb4k3xvj4BOaUhRffFfyq/WX26QOJ2E3P3xtKmMfJ3LjoEJ7iz0Do8NAfjwShu9
4+RS6wwR1qDMAzRau9Wsx6LbPt/JMpHf51/0MbCrfhgEAgPLjDUR+/7nrJCk3R5uDKTi
FjguMbnDh7nkFp03IVgkV/ehTVO4IDU/Cb4vKrSxNfs6n1EPaS9YHH9N+NtSU3m/XObv
NR9/JNO/WP0L4qIPuKk5hxuSycYgo0lKFKg+zyGiauu54hL5b4tCvvDRAIQql/jtG7QT
Jx1i19Gy+XWUBAwQme3t+UjE2WAoksAUuFJk7XCJO2rx5hGhq2ccpRsoOhFA1nZl4fc7
0/3Q==
d=1e100.net; s=20130820;
h=x-gm-message-state:mime-version:date:message-id:subject:from:to;
bh=5x6aY/1e/aVULsUro7a4B0vTbUG2NcmiHvrStddTlnc=;
b=i/r79NCjbpyCJXIljXMeFIUJdW35Xn4BF7E0gWHkALGDChEbJe1It52dJby/XgRvDE
a9LPE/XKs8+zRyrT24n9/ND17ezO7nanCNZyUdr21i12Jte6R0ke+m7ejDlQ8PPbNdvm
pGxTVrjHYvaqNQWeujl6KDFCQQ1t9O8qr71kXD7dCLipi2uTNtNHCdzafSK3nXMimg00
/pLIddNg5K7c1L+sIkDQkHh1AH5oETopaQetFZQzgzQAKwFMskIpIN3LmEw7hPczVtQm
3DjlKZcUBExG7d0pLaCZa6tlm1iNQW9Bwr/Vumb4D2njRxSlBBcXsYIpiViOGvuaIOB5
RPIQ==

11:09 AM (1 hour ago)

 to me
Delivery to the following recipient failed permanently:

kdhah@ucsc.edu

Technical details of permanent failure:
Google tried to deliver your message, but it was rejected by the server for the recipient domain ucsc.edu by aspmx.l.google.com. [2607:f8b0:400c:c0f::1a].

11:09 AM (1 hour ago)

 to me
Translate message
Turn off for: Norwegian
Delivery to the following recipient failed permanently:

lwright27@jhu.edu

Technical details of permanent failure:
Google tried to deliver your message, but it was rejected by the server for the recipient domain jhu.edu by smtp.johnshopkins.edu. [162.129.198.15].

The error that the other server returned was:

11:09 AM (1 hour ago)

 to me
Delivery to the following recipient failed permanently:

mriordan@ucsc.edu

Technical details of permanent failure:
Google tried to deliver your message, but it was rejected by the server for the recipient domain ucsc.edu by aspmx.l.google.com. [2607:f8b0:400c:c0f::1a].

11:09 AM (1 hour ago)

 to me
Translate message
Turn off for: French
Delivery to the following recipient failed permanently:

rwestb@jhu.edu

Technical details of permanent failure:
Google tried to deliver your message, but it was rejected by the server for the recipient domain jhu.edu by smtp.johnshopkins.edu. [162.129.198.15].

The error that the other server returned was:

11:09 AM (1 hour ago)

 to me
Delivery to the following recipient failed permanently:

rscherba@ucsc.edu

Technical details of permanent failure:
Google tried to deliver your message, but it was rejected by the server for the recipient domain ucsc.edu by aspmx.l.google.com. [2607:f8b0:400c:c0f::1a].

11:09 AM (1 hour ago)

 to me
Delivery to the following recipient failed permanently:

kang@uchicago.edu

Technical details of permanent failure:
Google tried to deliver your message, but it was rejected by the server for the recipient domain uchicago.edu by mailgateway03.uchicago.edu. [128.135.107.104].

11:09 AM (1 hour ago)

 to me
Translate message
Turn off for: French
Delivery to the following recipient failed permanently:

sbatiuk1@jhu.edu

Technical details of permanent failure:
Google tried to deliver your message, but it was rejected by the server for the recipient domain jhu.edu by smtp.johnshopkins.edu. [162.129.198.15].

The error that the other server returned was:

11:09 AM (1 hour ago)

 to me
Delivery to the following recipient failed permanently:

kramanan@andrew.cmu.edu

Technical details of permanent failure:
Google tried to deliver your message, but it was rejected by the server for the recipient domain andrew.cmu.edu by andrew-mx-03.andrew.cmu.edu. [128.2.10.137].

The error that the other server returned was:
553 5.3.0 <mgray@andrew.cmu.edu>… The email account that you tried to reach does not exist.  Please try double-checking the recipient’s email address for typos or unnecessary spaces.

11:09 AM (1 hour ago)

 to me
Delivery to the following recipient failed permanently:

11:09 AM (1 hour ago)

 to me
Delivery to the following recipient failed permanently:

kzollman@cmu.edu

Technical details of permanent failure:
Google tried to deliver your message, but it was rejected by the server for the recipient domain cmu.edu by cmu-mx-04.andrew.cmu.edu. [128.2.155.69].

The error that the other server returned was:
553 5.3.0 <mblum@cmu.edu>… The email account that you tried to reach does not exist.  Please try double-checking the recipient’s email address for typos or unnecessary spaces.

11:09 AM (1 hour ago)

 to me
Delivery to the following recipient failed permanently:

rutesacate@uem.mz

Technical details of permanent failure:
Google tried to deliver your message, but it was rejected by the server for the recipient domain uem.mz by webmail.uem.mz. [196.3.96.30].

11:09 AM (1 hour ago)

 to me
Delivery to the following recipient failed permanently:

kmortens@ucsc.edu

Technical details of permanent failure:
Google tried to deliver your message, but it was rejected by the server for the recipient domain ucsc.edu by aspmx.l.google.com. [2607:f8b0:400c:c0f::1a].

11:09 AM (1 hour ago)

 to me
Delivery to the following recipient failed permanently:

sendsen@cmu.edu

Technical details of permanent failure:
Google tried to deliver your message, but it was rejected by the server for the recipient domain cmu.edu by cmu-mx-04.andrew.cmu.edu. [128.2.155.69].

The error that the other server returned was:
553 5.3.0 <mblum@cmu.edu>… The email account that you tried to reach does not exist.  Please try double-checking the recipient’s email address for typos or unnecessary spaces.

11:09 AM (1 hour ago)

 to me
Delivery to the following recipient failed permanently:

safaa.bashir@guc.edu.eg

Technical details of permanent failure:
Google tried to deliver your message, but it was rejected by the server for the recipient domain guc.edu.eg by ironport.guc.edu.eg. [62.241.151.163].

The error that the other server returned was:

—– Original message —–

DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed;
d=gmail.com; s=20120113;
h=mime-version:date:message-id:subject:from:to;
bh=5x6aY/1e/aVULsUro7a4B0vTbUG2NcmiHvrStddTlnc=;
b=FGnMb4k3xvj4BOaUhRffFfyq/WX26QOJ2E3P3xtKmMfJ3LjoEJ7iz0Do8NAfjwShu9
4+RS6wwR1qDMAzRau9Wsx6LbPt/JMpHf51/0MbCrfhgEAgPLjDUR+/7nrJCk3R5uDKTi
FjguMbnDh7nkFp03IVgkV/ehTVO4IDU/Cb4vKrSxNfs6n1EPaS9YHH9N+NtSU3m/XObv
NR9/JNO/WP0L4qIPuKk5hxuSycYgo0lKFKg+zyGiauu54hL5b4tCvvDRAIQql/jtG7QT
Jx1i19Gy+XWUBAwQme3t+UjE2WAoksAUuFJk7XCJO2rx5hGhq2ccpRsoOhFA1nZl4fc7
0/3Q==
d=1e100.net; s=20130820;
h=x-gm-message-state:mime-version:date:message-id:subject:from:to;
bh=5x6aY/1e/aVULsUro7a4B0vTbUG2NcmiHvrStddTlnc=;
b=Hv48vvXdibWp15juRRM2pE8sPRyQRhLhjYHBTajXV3bhBMlS/0iLqQKNPDasnRzKSS
uvuthrs9PohLxaqdfDr1xNd8XyXP1KQz2GwBSJImaEkj/Lqc5FWU1D/ve+0oPDYto93N
YTKJJbC0s/Rh42T0p9uahfRKAeY45VBU8vfG0P9RX0vDQ3jJ3GrHdDYvFzE+n0DVuax6
ViX8cQxnC9MAWIQ2YPwYVIQHogPWPBuNXypCf+Yxh649tcC4fW2zchnL1BrJyqFA14hn
sqDVfbk2KXmU730QLdlV+8OQZThIFerlNyQfUV8xI9sL7dbZ7cFUzj616yv2uEvXGUyj
wOtA==

11:09 AM (1 hour ago)

 to me
Delivery to the following recipient failed permanently:

11:09 AM (1 hour ago)

 to me
Delivery to the following recipient failed permanently:

11:09 AM (1 hour ago)

 to me
Delivery to the following recipient failed permanently:

11:09 AM (1 hour ago)

 to me
Delivery to the following recipient failed permanently:

jzal@phas.ubc.ca

Technical details of permanent failure:
Google tried to deliver your message, but it was rejected by the server for the recipient domain phas.ubc.ca by vma.mail-relay.ubc.ca. [142.103.226.211].

The error that the other server returned was:
550 5.1.1 <pallab@phas.ubc.ca>: Recipient address rejected: undeliverable address: host mail.phas.ubc.ca[142.103.236.13] said: 550 5.1.1 <pallab@phas.ubc.ca>… User unknown (in reply to RCPT TO command)

—– Original message —–

DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed;
d=gmail.com; s=20120113;
h=mime-version:date:message-id:subject:from:to;
bh=5x6aY/1e/aVULsUro7a4B0vTbUG2NcmiHvrStddTlnc=;
b=FGnMb4k3xvj4BOaUhRffFfyq/WX26QOJ2E3P3xtKmMfJ3LjoEJ7iz0Do8NAfjwShu9
4+RS6wwR1qDMAzRau9Wsx6LbPt/JMpHf51/0MbCrfhgEAgPLjDUR+/7nrJCk3R5uDKTi
FjguMbnDh7nkFp03IVgkV/ehTVO4IDU/Cb4vKrSxNfs6n1EPaS9YHH9N+NtSU3m/XObv
NR9/JNO/WP0L4qIPuKk5hxuSycYgo0lKFKg+zyGiauu54hL5b4tCvvDRAIQql/jtG7QT
Jx1i19Gy+XWUBAwQme3t+UjE2WAoksAUuFJk7XCJO2rx5hGhq2ccpRsoOhFA1nZl4fc7
0/3Q==
d=1e100.net; s=20130820;
h=x-gm-message-state:mime-version:date:message-id:subject:from:to;
bh=5x6aY/1e/aVULsUro7a4B0vTbUG2NcmiHvrStddTlnc=;
b=ezfEOn0VTQR11rW/Y+ye4qRhbpKPukMi3/QUXjlQVxOhtG6enlM7fRhwzFo17nkLJP
LnEtXNmp9E9+8m4XNwbXyJm2Q5T8z+TeWRufvz4Ip65tyBEBU2SaxWB/ksygW/XXKMq5
EJlb6IULVjlS3vbP4ejbjSLecRTsS8Gwu+4/DqnyVT+iCuOEoNoqi1z//9QJ553DxLJx
Ud1ZaVPOJk+VFdLbr/zavJR634ExgKtQ1xrkjRikw4ddcYBH21Obr5oM+13ND5HStKWE
eoG9nQmmesuuvmMiVdytzdvudKdOn06MVwIlA/sRSH3Pz3X3KNsI1VN8OJqi0QEnZ3nl
RhJg==

11:09 AM (1 hour ago)

 to me
Delivery to the following recipient failed permanently:

moborski@andrew.cmu.edu

Technical details of permanent failure:
Google tried to deliver your message, but it was rejected by the server for the recipient domain andrew.cmu.edu by andrew-mx-01.andrew.cmu.edu. [128.2.10.117].

The error that the other server returned was:
553 5.3.0 <sg23@andrew.cmu.edu>… The email account that you tried to reach does not exist.  Please try double-checking the recipient’s email address for typos or unnecessary spaces.

—– Original message —–

DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed;
d=gmail.com; s=20120113;
h=mime-version:date:message-id:subject:from:to;
bh=5x6aY/1e/aVULsUro7a4B0vTbUG2NcmiHvrStddTlnc=;
b=FGnMb4k3xvj4BOaUhRffFfyq/WX26QOJ2E3P3xtKmMfJ3LjoEJ7iz0Do8NAfjwShu9
4+RS6wwR1qDMAzRau9Wsx6LbPt/JMpHf51/0MbCrfhgEAgPLjDUR+/7nrJCk3R5uDKTi
FjguMbnDh7nkFp03IVgkV/ehTVO4IDU/Cb4vKrSxNfs6n1EPaS9YHH9N+NtSU3m/XObv
NR9/JNO/WP0L4qIPuKk5hxuSycYgo0lKFKg+zyGiauu54hL5b4tCvvDRAIQql/jtG7QT
Jx1i19Gy+XWUBAwQme3t+UjE2WAoksAUuFJk7XCJO2rx5hGhq2ccpRsoOhFA1nZl4fc7
0/3Q==
d=1e100.net; s=20130820;
h=x-gm-message-state:mime-version:date:message-id:subject:from:to;
bh=5x6aY/1e/aVULsUro7a4B0vTbUG2NcmiHvrStddTlnc=;
b=LB0F1lP9a4hOkF4C6uexYLUtM0/dRB6tkTvbjVVo7U+6RLlDAv4Hs1yPXMgx91u5+p
RxOVEBRZi7eIuMtYijxxNa6lCi1T0EZ67VFXy5TQKdogGVl6cSGLCf7pRbphKtiDSKRS
4mAfnkn+dGJV0tXMAjNEjG5la1GGSW+2TriUEpwBRnNH2XZaCRxGXvLEd8tienACPgr9
3z52pg4LkkyZ9dKKX9Fsp7fVMkK4SEq/g5WOzld48d56kPvmOH+A/YLWLk/LpozLQT20
6i+tp6x1A/k/rTaMtF2tklSXxgk3iqGA4BMuU7uZJ6SF/6wHvLOAAM2xNvPIubHxr9Kk
RQNw==

11:09 AM (1 hour ago)

 to me
Delivery to the following recipient failed permanently:

pallab@phas.ubc.ca

Technical details of permanent failure:
Google tried to deliver your message, but it was rejected by the server for the recipient domain phas.ubc.ca by vma.mail-relay.ubc.ca. [142.103.226.211].

11:09 AM (1 hour ago)

 to me
Delivery to the following recipient failed permanently:

liy@andrew.cmu.edu

Technical details of permanent failure:
Google tried to deliver your message, but it was rejected by the server for the recipient domain andrew.cmu.edu by andrew-mx-01.andrew.cmu.edu. [128.2.10.117].

11:09 AM (1 hour ago)

 to me
Delivery to the following recipient failed permanently:

11:09 AM (1 hour ago)

 to me
Delivery to the following recipient failed permanently:

11:09 AM (1 hour ago)

 to me
Delivery to the following recipient failed permanently:

john.beatty@interchange.ubc.ca

Technical details of permanent failure:
Google tried to deliver your message, but it was rejected by the server for the recipient domain interchange.ubc.ca by vma.mail-relay.ubc.ca. [142.103.226.211].

The error that the other server returned was:
550 5.1.1 <john.beatty@interchange.ubc.ca>: Recipient address rejected: undeliverable address: host mx-out.mail-relay.ubc.ca[142.103.226.213] said: 550 5.1.1 <john.beatty@interchange.ubc.ca>: Recipient address rejected: User unknown in virtual alias table (in reply to RCPT TO command)

—– Original message —–

DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed;
d=gmail.com; s=20120113;
h=mime-version:date:message-id:subject:from:to;
bh=5x6aY/1e/aVULsUro7a4B0vTbUG2NcmiHvrStddTlnc=;
b=FGnMb4k3xvj4BOaUhRffFfyq/WX26QOJ2E3P3xtKmMfJ3LjoEJ7iz0Do8NAfjwShu9
4+RS6wwR1qDMAzRau9Wsx6LbPt/JMpHf51/0MbCrfhgEAgPLjDUR+/7nrJCk3R5uDKTi
FjguMbnDh7nkFp03IVgkV/ehTVO4IDU/Cb4vKrSxNfs6n1EPaS9YHH9N+NtSU3m/XObv
NR9/JNO/WP0L4qIPuKk5hxuSycYgo0lKFKg+zyGiauu54hL5b4tCvvDRAIQql/jtG7QT
Jx1i19Gy+XWUBAwQme3t+UjE2WAoksAUuFJk7XCJO2rx5hGhq2ccpRsoOhFA1nZl4fc7
0/3Q==
d=1e100.net; s=20130820;
h=x-gm-message-state:mime-version:date:message-id:subject:from:to;
bh=5x6aY/1e/aVULsUro7a4B0vTbUG2NcmiHvrStddTlnc=;
b=hW9TEl+OFC+VYufoWOgHcY0WhqDOKgx367YBKLuMbVQT0etkY7d2ZrQsf9knTicSVL
ZaKnfA80BBKPiZUwfysdpfCh0p/FfnN09gJnkkpiJERjujTsbS49Jf3R6JhLw84lsQ/w
RHNmdiTlQfdNsniOB/1L8BNbHAV9Jv3Y7ehA/8T+OuxBLkhHry9SgMdVpSE6TGo5jRZ9
pt7TL9m74Q9twJYKTofNUBuO9AH+LT128ikdiRtAYHrlgR8ljX87cKUyeoxvQj3vdsDD
BlqC13GGydeTUfQ9NNhY9knSiYMZRqcqRWuGA1AHotEK1dhYy1UeaW30nARhaJYxtHp0
uM/Q==

11:09 AM (1 hour ago)

 to me
Delivery to the following recipient failed permanently:

kbandura@andrew.cmu.edu

Technical details of permanent failure:
Google tried to deliver your message, but it was rejected by the server for the recipient domain andrew.cmu.edu by andrew-mx-01.andrew.cmu.edu. [128.2.10.117].

11:09 AM (1 hour ago)

 to me
Delivery to the following recipient failed permanently:

11:09 AM (1 hour ago)

 to me
Delivery to the following recipient failed permanently:

### postmaster@vch.ca

11:09 AM (1 hour ago)

 to me

Delivery has failed to these recipients or distribution lists:

john.aldrich@vch.ca
The recipient’s e-mail address was not found in the recipient’s e-mail system. Microsoft Exchange will not try to redeliver this message for you. Please check the e-mail address and try resending this message, or provide the following diagnostic text to your system administrator.

Sent by Microsoft Exchange Server 2007

Generating server: vch.ca

john.aldrich@vch.ca

Received: from relay-ex4.vch.ca (10.29.227.131) by vchexhtp1.vch.ca
(139.173.21.65) with Microsoft SMTP Server id 8.3.327.1; Tue, 22 Mar 2016
11:09:20 -0700
Received: from relay-ex4.vch.ca (unknown [127.0.0.1])	by IMSVA (Postfix) with
ESMTP id 2E2EA128059	for <john.aldrich@vch.ca>; Tue, 22 Mar 2016 11:07:27
-0700 (PDT)
relay-ex4.vch.ca (Postfix) with ESMTP id BEB01128056	for
<john.aldrich@vch.ca>; Tue, 22 Mar 2016 11:07:26 -0700 (PDT)
<john.aldrich@vch.ca>; Tue, 22 Mar 2016 11:09:18 -0700 (PDT)
DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed;
d=gmail.com; s=20120113;
h=mime-version:date:message-id:subject:from:to;
bh=5x6aY/1e/aVULsUro7a4B0vTbUG2NcmiHvrStddTlnc=;
b=FGnMb4k3xvj4BOaUhRffFfyq/WX26QOJ2E3P3xtKmMfJ3LjoEJ7iz0Do8NAfjwShu9
4+RS6wwR1qDMAzRau9Wsx6LbPt/JMpHf51/0MbCrfhgEAgPLjDUR+/7nrJCk3R5uDKTi
FjguMbnDh7nkFp03IVgkV/ehTVO4IDU/Cb4vKrSxNfs6n1EPaS9YHH9N+NtSU3m/XObv
NR9/JNO/WP0L4qIPuKk5hxuSycYgo0lKFKg+zyGiauu54hL5b4tCvvDRAIQql/jtG7QT
Jx1i19Gy+XWUBAwQme3t+UjE2WAoksAUuFJk7XCJO2rx5hGhq2ccpRsoOhFA1nZl4fc7
0/3Q==
d=1e100.net; s=20130820;
h=x-gm-message-state:mime-version:date:message-id:subject:from:to;
bh=5x6aY/1e/aVULsUro7a4B0vTbUG2NcmiHvrStddTlnc=;
b=h+RpXCxBI4xd8BAbIu4P0+JxXFzkKHXywosW955fOjBFLAK9R49y1MOc7T8po3Lb9e
KXlS1/hj5/a6VFvAvSBIuI1IKxtP3fgSF3j+sXYhi0nfjtWah7mQPgCRigMWrHvcBN6P
LduWfANC7wsjLfWOvpW42z/aToQSiw3kWQDdSDrXDJs1VTAmkH1k7QAhBnwyDTNrD18U
PERH/Aie41FGJ+qS2QucUx4hkWyb34oHHeXJg9JqUwBbp3VFy+nmh6+m32ekLVU+kEok
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zAeg==
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Message-ID: <CAOKUxJBApka+wV4-R2nY6UkNdDF36=nFw7otMYBTodK=XB1+zQ@mail.gmail.com>
Subject: ZULF MODEL FITS LAST TRADE VOLATILITY SURFACE BETTER THAN HESTON
MODEL IN MORE THAN 90% IN 56 CASES
From: "zulfikar.ahmed@gmail.com" <zulfikar.ahmed@gmail.com>
To: <jfrenkel@fma.if.usp.br>, <jhansen@uchicago.edu>,
<jharrington@uchicago.edu>, <jharris@andrew.cmu.edu>, <jhp@uchicago.edu>,
<jhricko_4@juno.com>, <jhs@math.ubc.ca>, <jhutasoi@andrew.cmu.edu>,
<jianjunp@andrew.cmu.edu>, <jinha@uchicago.edu>, <jjbrehm@uchicago.edu>,
<jlind@andrew.cmu.edu>, <jlondon@uchicago.edu>, <jlw@jhu.edu>,
<jmateo@uchicago.edu>, <jmerseth@uchicago.edu>, <jmetcalf@ucsc.edu>,
<jmg@uchicago.edu>, <jmogel@ucsc.edu>, <joel@scipp.ucsc.edu>,
<joelms@andrew.cmu.edu>, <john.aldrich@vch.ca>,
<john.beatty@interchange.ubc.ca>, <johncrawford53@hotmail.com>,
<jose.oliveira@dfn.if.usp.br>, <josesoto@uem.mz>, <josue@fma.if.usp.br>,
<jpino@andrew.cmu.edu>, <jpitts@uchicago.edu>, <jpl@stat.cmu.edu>,
<jpmccorm@uchicago.edu>, <jr67@andrew.cmu.edu>, <jrsteinb@illinois.edu>,
<js5m@andrew.cmu.edu>, <js6n@andrew.cmu.edu>, <jsamuels@ucsc.edu>,
<jthome@andrew.cmu.edu>, <julia_krause13@hotmail.com>, <jzal@phas.ubc.ca>,
<kang@uchicago.edu>, <karu@math.ubc.ca>, <kbandura@andrew.cmu.edu>,
<kboyd@uchicago.edu>, <kculp@midway.uchicago.edu>, <kdhah@ucsc.edu>,
<kebelsduggan@northwestern.edu>, <keisha@uchicago.edu>,
<keith.miller@bue.edu.eg>, <kelbyharrison@northwestern.edu>,
<keshet@math.ubc.ca>, <khaled.alshamouty@guc.edu.eg>, <khan@uchicago.edu>,
<khosravi@math.ubc.ca>, <kiefl@triumf.ca>, <kimberleab@yahoo.com>,
<kiyohara@fge.if.usp.br>, <kkoch@andrew.cmu.edu>, <klein@andrew.cmu.edu>,
<kliu@math.ubc.ca>, <km3b@andrew.cmu.edu>, <kmoriya@andrew.cmu.edu>,
<kmortens@ucsc.edu>, <knwoods@cmu.edu>, <konoplya@fma.if.usp.br>,
<kouslaa@uchicago.edu>, <kramanan@andrew.cmu.edu>, <kramkov@andrew.cmu.edu>,
<ksanders@illinois.edu>, <kunalghosh@cmu.edu>, <kurnikova@cmu.edu>,
<kwarman@andrew.cmu.edu>, <kwiat@illinois.edu>, <kxrobert@ucsc.edu>,
<kzollman@cmu.edu>, <l-wedeen@uchicago.edu>, <lamy@if.usp.br>,
<LauraPapish2010@northwestern.edu>, <laurel@andrew.cmu.edu>,
<lberger@andrew.cmu.edu>, <lburkhdl@interchange.ubc.ca>,
<lchamon@dfn.if.usp.br>, <lchristo@andrew.cmu.edu>, <lesurea@uchicago.edu>,
<levine@psc.edu>, <levineweinberg@uchicago.edu>, <lewis@ucsc.edu>,
<lfli@andrew.cmu.edu>, <lievers1@jhu.edu>, <limauro@andrew.cmu.edu>,
<lincolnw@andrew.cmu.edu>, <linda.brown@jhu.edu>, <liy@andrew.cmu.edu>,
<llinas@andrew.cmu.edu>, <lpalmer@andrew.cmu.edu>, <lskarsga@bccancer.bc.ca>,
<lsolum@illinois.edu>, <luxmi@andrew.cmu.edu>, <lvuocolo@andrew.cmu.edu>,
<lwright27@jhu.edu>, <m-mullins@northwestern.edu>, <m-nayfeh@illinois.edu>,
<m-silverstein@uchicago.edu>, <m-stone5@illinois.edu>, <maclean@math.ubc.ca>,
<magro@fma.if.usp.br>, <magyar@math.ubc.ca>, <maishamiss@gmail.com>,
<makins@illinois.edu>, <mandal@andrew.cmu.edu>, <marchett@if.usp.br>,
<margolis@interchange.ubc.ca>, <martha_nussbaum@uchicago.edu>,
<math@math.ubc.ca>, <matsuoka@dfn.if.usp.br>, <mav@physics.ubc.ca>,
<maxcherem2012@northwestern.edu>, <maydede@interchange.ubc.ca>,
<mbier@andrew.cmu.edu>, <mbloom@uchicago.edu>, <mblum@cmu.edu>,
<mbspencer@uchicago.edu>, <mbw@illinois.edu>, <mcdawson@uchicago.edu>,
<meierding@uchicago.edu>, <mestre@illinois.edu>,
<mfishban@midway.uchicago.edu>, <mfrise@ucsc.edu>, <mg0c@andrew.cmu.edu>,
<mghartlie@hotmail.com>, <mgomes@fma.if.usp.br>, <mgp@illinois.edu>,
<mgray@andrew.cmu.edu>, <mharrell@cmu.edu>, <mhassan@bue.edu.eg>,
<mmuramat@if.usp.br>, <moborski@andrew.cmu.edu>,
<monteiro@uchicago.edu>, <moor302@yahoo.com>, <moore8@andrew.cmu.edu>,
<morris@jhu.edu>, <mpato@fma.if.usp.br>, <mriordan@ucsc.edu>,
<mund@fma.if.usp.br>, <muthu@uchicago.edu>, <muwenk@andrew.cmu.edu>,
<mweems@andrew.cmu.edu>, <mwilliams@jhu.edu>, <n-tarcov@uchicago.edu>,
<nassif@math.ubc.ca>, <nbaker@andrew.cmu.edu>, <nelson.carlin@dfn.if.usp.br>,
<ness@math.ubc.ca>, <neufeld@pha.jhu.edu>, <nermeen.serag@guc.edu.eg>,
<nguyentrh@northwestern.edu>, <nhassoun@andrew.cmu.edu>, <njb@math.ubc.ca>,
<nmisra@andrew.cmu.edu>, <noelw@andrew.cmu.edu>, <nsissons@andrew.cmu.edu>,
<o-maksymchuk@northwestern.edu>, <ocanter@ucsc.edu>, <oliveira@if.usp.br>,
<omar.karam@bue.edu.eg>, <p-deutscher@northwestern.edu>,
<pallab@phas.ubc.ca>, Paul Roth <paroth@ucsc.edu>, <passos@fma.if.usp.br>,
<patrick.leland@jhu.edu>, <paujaramillo@if.usp.br>, <paulini@cmu.edu>,
<pbooke@uchicago.edu>, <pcooke1@andrew.cmu.edu>, <pdelner1@jhu.edu>,
<pdf@pha.jhu.edu>, <peirce@math.ubc.ca>, <pengzhen@andrew.cmu.edu>,
<perkins@math.ubc.ca>, <peteanu@andrew.cmu.edu>, <peter@physics.ucsc.edu>,
<peterjludlow@northwestern.edu>, <peterson@math.ubc.ca>,
<petrov@fma.if.usp.br>, <pgaraud@soe.ucsc.edu>, <pikhurko@andrew.cmu.edu>,
<pilchman@ucsc.edu>, <pisztora@andrew.cmu.edu>, <piza@fma.if.usp.br>,
<pjguerns@ucsc.edu>, <pmarkell@uchicago.edu>, <profkatz@gmail.com>,
<profumo@scipp.ucsc.edu>, <pshekhar@andrew.cmu.edu>, <pstojan2@jhu.edu>,
<pvisser@uchicago.edu>, <randersn@interchange.ubc.ca>,
<rasha.emara@guc.edu.eg>, <rballari@interchange.ubc.ca>, <rbett1@jhu.edu>,
<rblock@andrew.cmu.edu>, <rbriere@andrew.cmu.edu>, <rcarroll@andrew.cmu.edu>,
<rch@pha.jhu.edu>, <rclegg@illinois.edu>, <rcroft@andrew.cmu.edu>,
<rcummins@illinois.edu>, <reichst@math.ubc.ca>, <rf51@cmu.edu>,
<rfroese@math.ubc.ca>, <rgil@andrew.cmu.edu>, <rgleigh@illinois.edu>,
<rgoel@uchicago.edu>, <rha@ucsc.edu>, <richer@astro.ubc.ca>,
<rjasnow@jhu.edu>, <rjohnson@scipp.ucsc.edu>, <rk1t@andrew.cmu.edu>,
<rkelanic@uchicago.edu>, <rkraut1@northwestern.edu>, <rm1o@andrew.cmu.edu>,
<rm5g@andrew.cmu.edu>, <rmedelstein@gmail.com>, <robilotta@dfn.if.usp.br>,
<robtg@ucsc.edu>, <rolfsen@math.ubc.ca>, <ronan@jhu.edu>,
<rongchao@andrew.cmu.edu>, <rose@phas.ubc.ca>, <roth99@illinois.edu>,
<rscherba@ucsc.edu>, <rshd@uchicago.edu>, <rstewart@andrew.cmu.edu>,
<russg@illinois.edu>, <rutesacate@uem.mz>, <ruthrichardmoore@comcast.net>,
<rvribas@dfn.if.usp.br>, <rwestb@jhu.edu>, <ryan5@jhu.edu>,
<ryanbdoran@northwestern.edu>, <s-ebelsduggan@northwestern.edu>,
Anna <sanna@andrew.cmu.edu>, <sara@cmu.edu>, <savitt@interchange.ubc.ca>,
<sbatiuk1@jhu.edu>, <sbchavel@uchicago.edu>, <russ@cmphys.phys.cmu.edu>,
<sberrym@interchange.ubc.ca>, <sbevel@uchicago.edu>, <scheines@cmu.edu>,
<schneider@cmu.edu>, <schoetzau@math.ubc.ca>, <schonbek@ucsc.edu>,
<schulten@illinois.edu>, <schumacher@ernest.phys.cmu.edu>,
<scoopbd@gmail.com>, <sdasgup2@ucsc.edu>, <sef@cs.cmu.edu>,
<sej@uchicago.edu>, <selvin@illinois.edu>, <sendsen@cmu.edu>,
<serrede@illinois.edu>, <sethmayer2014@northwestern.edu>, <sev@uchicago.edu>,
<sfenner@uchicago.edu>, <sfli@andrew.cmu.edu>, <sg23@andrew.cmu.edu>,
<sgalloway@uchicago.edu>, <sgm@uchicago.edu>, <sgraul@andrew.cmu.edu>,
<sgross11@jhu.edu>, <shlomo@andrew.cmu.edu>, David Shwayder
<shwayder@illinois.edu>, <sieg@cmu.edu>, <simchen@interchange.ubc.ca>,
<simons@andrew.cmu.edu>, <sisotani@fge.if.usp.br>, <skoplik1@jhu.edu>,
<slcooper@illinois.edu>, james P <strivergreen@gmail.com>,
<bm@falconfone.com>
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Return-Path: zulfikar.ahmed@gmail.com


Original-Recipient: rfc822;john.aldrich@vch.ca
Final-Recipient: rfc822;john.aldrich@vch.ca
Action: failed
Status: 5.1.1

———- Forwarded message ———-
From: “zulfikar.ahmed@gmail.com” <zulfikar.ahmed@gmail.com>
To: <jfrenkel@fma.if.usp.br>, <jhansen@uchicago.edu>, <jharrington@uchicago.edu>, <jharris@andrew.cmu.edu>, <jhp@uchicago.edu>, <jhricko_4@juno.com>, <jhs@math.ubc.ca>, <jhutasoi@andrew.cmu.edu>, <jianjunp@andrew.cmu.edu>, <jinha@uchicago.edu>, <jjbrehm@uchicago.edu>, <jlind@andrew.cmu.edu>, <jlondon@uchicago.edu>, <jlw@jhu.edu>, <jmateo@uchicago.edu>, <jmerseth@uchicago.edu>, <jmetcalf@ucsc.edu>, <jmg@uchicago.edu>, <jmogel@ucsc.edu>, <joel@scipp.ucsc.edu>, <joelms@andrew.cmu.edu>, <john.aldrich@vch.ca>, <john.beatty@interchange.ubc.ca>, <johncrawford53@hotmail.com>, <jose.oliveira@dfn.if.usp.br>, <josesoto@uem.mz>, <josue@fma.if.usp.br>, <jpadgett@uchicago.edu>, <jpbalz@uchicago.edu>, <jperuma1@jhu.edu>, <jpino@andrew.cmu.edu>, <jpitts@uchicago.edu>, <jpl@stat.cmu.edu>, <jpmccorm@uchicago.edu>, <jr67@andrew.cmu.edu>, <jrsteinb@illinois.edu>, <js5m@andrew.cmu.edu>, <js6n@andrew.cmu.edu>, <jsamuels@ucsc.edu>, <jthome@andrew.cmu.edu>, <julia_krause13@hotmail.com>, <jzal@phas.ubc.ca>, <kang@uchicago.edu>, <karu@math.ubc.ca>, <kbandura@andrew.cmu.edu>, <kboyd@uchicago.edu>, <kculp@midway.uchicago.edu>, <kdhah@ucsc.edu>, <kebelsduggan@northwestern.edu>, <keisha@uchicago.edu>, <keith.miller@bue.edu.eg>, <kelbyharrison@northwestern.edu>, <keshet@math.ubc.ca>, <khaled.alshamouty@guc.edu.eg>, <khan@uchicago.edu>, <khosravi@math.ubc.ca>, <kiefl@triumf.ca>, <kimberleab@yahoo.com>, <kiyohara@fge.if.usp.br>, <kkoch@andrew.cmu.edu>, <klein@andrew.cmu.edu>, <kliu@math.ubc.ca>, <km3b@andrew.cmu.edu>, <kmoriya@andrew.cmu.edu>, <kmortens@ucsc.edu>, <knwoods@cmu.edu>, <konoplya@fma.if.usp.br>, <kouslaa@uchicago.edu>, <kramanan@andrew.cmu.edu>, <kramkov@andrew.cmu.edu>, <ksanders@illinois.edu>, <kunalghosh@cmu.edu>, <kurnikova@cmu.edu>, <kwarman@andrew.cmu.edu>, <kwiat@illinois.edu>, <kxrobert@ucsc.edu>, <kzollman@cmu.edu>, <l-wedeen@uchicago.edu>, <lamy@if.usp.br>, <LauraPapish2010@northwestern.edu>, <laurel@andrew.cmu.edu>, <lberger@andrew.cmu.edu>, <lburkhdl@interchange.ubc.ca>, <lchamon@dfn.if.usp.br>, <lchristo@andrew.cmu.edu>, <lesurea@uchicago.edu>, <levine@psc.edu>, <levineweinberg@uchicago.edu>, <lewis@ucsc.edu>, <lfli@andrew.cmu.edu>, <lievers1@jhu.edu>, <limauro@andrew.cmu.edu>, <lincolnw@andrew.cmu.edu>, <linda.brown@jhu.edu>, <liy@andrew.cmu.edu>, <llinas@andrew.cmu.edu>, <lpalmer@andrew.cmu.edu>, <lskarsga@bccancer.bc.ca>, <lsolum@illinois.edu>, <luxmi@andrew.cmu.edu>, <lvuocolo@andrew.cmu.edu>, <lwright27@jhu.edu>, <m-mullins@northwestern.edu>, <m-nayfeh@illinois.edu>, <m-silverstein@uchicago.edu>, <m-stone5@illinois.edu>, <maclean@math.ubc.ca>, <magro@fma.if.usp.br>, <magyar@math.ubc.ca>, <maishamiss@gmail.com>, <makins@illinois.edu>, <mandal@andrew.cmu.edu>, <marchett@if.usp.br>, <margolis@interchange.ubc.ca>, <martha_nussbaum@uchicago.edu>, <math@math.ubc.ca>, <matsuoka@dfn.if.usp.br>, <mav@physics.ubc.ca>, <maxcherem2012@northwestern.edu>, <maydede@interchange.ubc.ca>, <mbier@andrew.cmu.edu>, <mbloom@uchicago.edu>, <mblum@cmu.edu>, <mbspencer@uchicago.edu>, <mbw@illinois.edu>, <mcdawson@uchicago.edu>, <meierding@uchicago.edu>, <mestre@illinois.edu>, <mfishban@midway.uchicago.edu>, <mfrise@ucsc.edu>, <mg0c@andrew.cmu.edu>, <mghartlie@hotmail.com>, <mgomes@fma.if.usp.br>, <mgp@illinois.edu>, <mgray@andrew.cmu.edu>, <mharrell@cmu.edu>, <mhassan@bue.edu.eg>, <mmuramat@if.usp.br>, <moborski@andrew.cmu.edu>, <mohamed.el-rafie@guc.edu.eg>, <mohammad@andrew.cmu.edu>, <monteiro@uchicago.edu>, <moor302@yahoo.com>, <moore8@andrew.cmu.edu>, <morris@jhu.edu>, <mpato@fma.if.usp.br>, <mriordan@ucsc.edu>, <mund@fma.if.usp.br>, <muthu@uchicago.edu>, <muwenk@andrew.cmu.edu>, <mweems@andrew.cmu.edu>, <mwilliams@jhu.edu>, <n-tarcov@uchicago.edu>, <nadra.sakr@guc.edu.eg>, <nagata@math.ubc.ca>, <narayan@physics.ucsc.edu>, <nassif@math.ubc.ca>, <nbaker@andrew.cmu.edu>, <nelson.carlin@dfn.if.usp.br>, <ness@math.ubc.ca>, <neufeld@pha.jhu.edu>, <nermeen.serag@guc.edu.eg>, <nguyentrh@northwestern.edu>, <nhassoun@andrew.cmu.edu>, <njb@math.ubc.ca>, <nmisra@andrew.cmu.edu>, <noelw@andrew.cmu.edu>, <nsissons@andrew.cmu.edu>, <o-maksymchuk@northwestern.edu>, <ocanter@ucsc.edu>, <oliveira@if.usp.br>, <omar.karam@bue.edu.eg>, <p-deutscher@northwestern.edu>, <pallab@phas.ubc.ca>, Paul Roth <paroth@ucsc.edu>, <passos@fma.if.usp.br>, <patrick.leland@jhu.edu>, <paujaramillo@if.usp.br>, <paulini@cmu.edu>, <pbooke@uchicago.edu>, <pcooke1@andrew.cmu.edu>, <pdelner1@jhu.edu>, <pdf@pha.jhu.edu>, <peirce@math.ubc.ca>, <pengzhen@andrew.cmu.edu>, <perkins@math.ubc.ca>, <peteanu@andrew.cmu.edu>, <peter@physics.ucsc.edu>, <peterjludlow@northwestern.edu>, <peterson@math.ubc.ca>, <petrov@fma.if.usp.br>, <pgaraud@soe.ucsc.edu>, <pikhurko@andrew.cmu.edu>, <pilchman@ucsc.edu>, <pisztora@andrew.cmu.edu>, <piza@fma.if.usp.br>, <pjguerns@ucsc.edu>, <pmarkell@uchicago.edu>, <profkatz@gmail.com>, <profumo@scipp.ucsc.edu>, <pshekhar@andrew.cmu.edu>, <pstojan2@jhu.edu>, <pvisser@uchicago.edu>, <randersn@interchange.ubc.ca>, <rasha.emara@guc.edu.eg>, <rballari@interchange.ubc.ca>, <rbett1@jhu.edu>, <rblock@andrew.cmu.edu>, <rbriere@andrew.cmu.edu>, <rcarroll@andrew.cmu.edu>, <rch@pha.jhu.edu>, <rclegg@illinois.edu>, <rcroft@andrew.cmu.edu>, <rcummins@illinois.edu>, <reichst@math.ubc.ca>, <rf51@cmu.edu>, <rfroese@math.ubc.ca>, <rgil@andrew.cmu.edu>, <rgleigh@illinois.edu>, <rgoel@uchicago.edu>, <rha@ucsc.edu>, <richer@astro.ubc.ca>, <rjasnow@jhu.edu>, <rjohnson@scipp.ucsc.edu>, <rk1t@andrew.cmu.edu>, <rkelanic@uchicago.edu>, <rkraut1@northwestern.edu>, <rm1o@andrew.cmu.edu>, <rm5g@andrew.cmu.edu>, <rmedelstein@gmail.com>, <robilotta@dfn.if.usp.br>, <robtg@ucsc.edu>, <rolfsen@math.ubc.ca>, <ronan@jhu.edu>, <rongchao@andrew.cmu.edu>, <rose@phas.ubc.ca>, <roth99@illinois.edu>, <rscherba@ucsc.edu>, <rshd@uchicago.edu>, <rstewart@andrew.cmu.edu>, <russg@illinois.edu>, <rutesacate@uem.mz>, <ruthrichardmoore@comcast.net>, <rvribas@dfn.if.usp.br>, <rwestb@jhu.edu>, <ryan5@jhu.edu>, <ryanbdoran@northwestern.edu>, <s-ebelsduggan@northwestern.edu>, <safaa.bashir@guc.edu.eg>, <salladin7@aol.com>, <sanchita@gmail.com>, Shelley Anna <sanna@andrew.cmu.edu>, <sara@cmu.edu>, <savitt@interchange.ubc.ca>, <sbatiuk1@jhu.edu>, <sbchavel@uchicago.edu>, <russ@cmphys.phys.cmu.edu>, <sberrym@interchange.ubc.ca>, <sbevel@uchicago.edu>, <scheines@cmu.edu>, <schneider@cmu.edu>, <schoetzau@math.ubc.ca>, <schonbek@ucsc.edu>, <schulten@illinois.edu>, <schumacher@ernest.phys.cmu.edu>, <scoopbd@gmail.com>, <sdasgup2@ucsc.edu>, <sef@cs.cmu.edu>, <sej@uchicago.edu>, <selvin@illinois.edu>, <sendsen@cmu.edu>, <serrede@illinois.edu>, <sethmayer2014@northwestern.edu>, <sev@uchicago.edu>, <sfenner@uchicago.edu>, <sfli@andrew.cmu.edu>, <sg23@andrew.cmu.edu>, <sgalloway@uchicago.edu>, <sgm@uchicago.edu>, <sgraul@andrew.cmu.edu>, <sgross11@jhu.edu>, <shlomo@andrew.cmu.edu>, David Shwayder <shwayder@illinois.edu>, <sieg@cmu.edu>, <simchen@interchange.ubc.ca>, <simons@andrew.cmu.edu>, <sisotani@fge.if.usp.br>, <skoplik1@jhu.edu>, <slade@math.ubc.ca>, <slamb@illinois.edu>, <slater@uchicago.edu>, <slcooper@illinois.edu>, james P <strivergreen@gmail.com>, <bm@falconfone.com>
Cc:
Date: Tue, 22 Mar 2016 11:09:16 -0700
Subject: ZULF MODEL FITS LAST TRADE VOLATILITY SURFACE BETTER THAN HESTON MODEL IN MORE THAN 90% IN 56 CASES

I am pleased to announce that our time-fractional Heston model fits the volatility surfaces determined by the LAST TRADE of call options statistically significantly better than the Heston model in 51/55 of the cases (stock/day) that I have checked last night.  The model differs from the Heston model by a single extra parameter 0<alpha<2.  The comparison is to calibrate both the Heston and Zulf models on a volatility surface and record the error of fit (sum of absolute difference of implied volatilities). The paired t-test of these errors give:

>>> ttest_rel(x.ix[:,2],x.ix[:,3])
(array(4.27139160907284), 7.7558339944524236e-05)

Here is the actual table of errors

UPL  2003-01-02  0.0957002682349182  0.0773492111916326
0   UPL  2003-01-03            0.078657        6.652813e-02
1   UPL  2003-01-06            0.069270        5.893240e-02
2   KMI  2002-02-08            0.007780        6.266435e-03
3   KMI  2002-02-11            0.008966        5.994275e-03
4   KMI  2002-02-12            0.008309        5.424351e-03
5   KMI  2002-02-13            0.007713        5.128947e-03
6   KMI  2002-02-14            0.005948        5.272464e-03
7   PAC  2006-11-21            0.000290        1.745138e-07
8   PAC  2006-11-22            0.000558        3.908786e-07
9   NFG  2003-01-02            0.088293        8.326848e-02
10  NFG  2003-01-03            0.092200        1.840495e-02
11  NFG  2003-01-06            0.082446        6.947264e-02
12  NFG  2003-01-07            0.089481        1.946255e-02
13  NFG  2003-01-08            0.091463        8.470383e-02
14  OXY  2002-02-08            0.034763        3.187211e-02
15  OXY  2002-02-11            0.029676        3.690711e-02
16  OXY  2002-02-12            0.022510        1.772629e-02
17  OXY  2002-02-13            0.017657        2.116841e-02
18  OXY  2002-02-14            0.024343        3.202859e-02
19  AEM  2002-02-08            0.123033        1.217102e-01
20  AEM  2002-02-11            0.110734        6.377745e-02
21  AEM  2002-02-12            0.100758        9.943284e-02
22  AEM  2002-02-13            0.088986        8.803400e-02
23  AEM  2002-02-14            0.103508        9.958264e-02
24  NWY  2006-10-11            0.005319        4.450291e-08
25  NWY  2006-10-12            0.001743        1.144806e-07
26  NWY  2006-10-13            0.004078        2.571337e-06
27  NWY  2006-10-16            0.004726        3.099954e-03
28  TEF  2002-02-08            0.010447        5.958070e-03
29  TEF  2002-02-11            0.009764        8.375140e-03
30  CIB  2006-08-18            0.001899        6.670807e-07
31  CIB  2006-08-21            0.001459        8.779171e-09
32  CIB  2006-08-22            0.004307        1.318464e-08
33  CIB  2006-08-23            0.006848        4.271603e-07
34  SKO  2002-02-08            0.059888        4.294716e-02
35  SKO  2002-02-11            0.061167        4.417510e-02
36  SKO  2002-02-12            0.061014        4.901067e-02
37  SKO  2002-02-13            0.055221        4.730380e-02
38  SKO  2002-02-14            0.061628        4.659908e-02
39  PAG  2007-07-03            0.005586        3.715073e-08
40  PAG  2007-07-05            0.008058        1.047600e-06
41  PAG  2007-07-06            0.007521        5.312208e-07
42  PAG  2007-07-09            0.007519        4.822871e-07
43  PAG  2007-07-10            0.006269        7.045978e-07
44  RBK  2002-02-08            0.119141        1.042945e-01
45  RBK  2002-02-11            0.128607        1.035408e-01
46  RBK  2002-02-12            0.131435        1.201102e-01
47  WGO  2002-02-08            0.109837        9.434335e-02
48  WGO  2002-02-11            0.094459        9.186975e-02
49  WGO  2002-02-12            0.109614        8.576695e-02
50  WGO  2002-02-13            0.110616        1.103984e-01
51  WGO  2002-02-14            0.116418        1.109057e-01
52  WAG  2002-02-08            0.059161        6.123514e-02
53  WAG  2002-02-11            0.067877        7.072952e-02
54  WAG  2002-02-12            0.073040        7.199622e-02
55  WAG  2002-02-13            0.060819        5.949971e-02

The situation is very similar to the great breakthrough of Black, Scholes and Merton whose model had a constant volatility assumption which everyone knew was not correct and did not hold in the sense that our alpha parameter is in theory constant per stock but the estimated alpha from last trade volatility surface is not constant.  A possibility that I might explore later is a third stochastic process for alpha but for now we have a clear model that is closed form, almost as fast as Heston model, and that improves the fit of Heston model overwhelmingly often (using last trades and not using bid-ask averages of option prices).
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Message-ID: <CAOKUxJBApka+wV4-R2nY6UkNdDF36=nFw7otMYBTodK=XB1+zQ@mail.gmail.com>
Subject: ZULF MODEL FITS LAST TRADE VOLATILITY SURFACE BETTER THAN HESTON
MODEL IN MORE THAN 90% IN 56 CASES
From: “zulfikar.ahmed@gmail.com” <zulfikar.ahmed@gmail.com>

slcooper@illinois.edu, james P <strivergreen@gmail.com>, bm@falconfone.com
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Date: Tue, 22 Mar 2016 11:09:16 -0700
Subject: ZULF MODEL FITS LAST TRADE VOLATILITY SURFACE BETTER THAN HESTON MODEL IN MORE THAN 90% IN 56 CASES

I am pleased to announce that our time-fractional Heston model fits the volatility surfaces determined by the LAST TRADE of call options statistically significantly better than the Heston model in 51/55 of the cases (stock/day) that I have checked last night.  The model differs from the Heston model by a single extra parameter 0<alpha<2.  The comparison is to calibrate both the Heston and Zulf models on a volatility surface and record the error of fit (sum of absolute difference of implied volatilities). The paired t-test of these errors give:

>>> ttest_rel(x.ix[:,2],x.ix[:,3])
(array(4.27139160907284), 7.7558339944524236e-05)

Here is the actual table of errors

UPL  2003-01-02  0.0957002682349182  0.0773492111916326
0   UPL  2003-01-03            0.078657        6.652813e-02
1   UPL  2003-01-06            0.069270        5.893240e-02
2   KMI  2002-02-08            0.007780        6.266435e-03
3   KMI  2002-02-11            0.008966        5.994275e-03
4   KMI  2002-02-12            0.008309        5.424351e-03
5   KMI  2002-02-13            0.007713        5.128947e-03
6   KMI  2002-02-14            0.005948        5.272464e-03
7   PAC  2006-11-21            0.000290        1.745138e-07
8   PAC  2006-11-22            0.000558        3.908786e-07
9   NFG  2003-01-02            0.088293        8.326848e-02
10  NFG  2003-01-03            0.092200        1.840495e-02
11  NFG  2003-01-06            0.082446        6.947264e-02
12  NFG  2003-01-07            0.089481        1.946255e-02
13  NFG  2003-01-08            0.091463        8.470383e-02
14  OXY  2002-02-08            0.034763        3.187211e-02
15  OXY  2002-02-11            0.029676        3.690711e-02
16  OXY  2002-02-12            0.022510        1.772629e-02
17  OXY  2002-02-13            0.017657        2.116841e-02
18  OXY  2002-02-14            0.024343        3.202859e-02
19  AEM  2002-02-08            0.123033        1.217102e-01
20  AEM  2002-02-11            0.110734        6.377745e-02
21  AEM  2002-02-12            0.100758        9.943284e-02
22  AEM  2002-02-13            0.088986        8.803400e-02
23  AEM  2002-02-14            0.103508        9.958264e-02
24  NWY  2006-10-11            0.005319        4.450291e-08
25  NWY  2006-10-12            0.001743        1.144806e-07
26  NWY  2006-10-13            0.004078        2.571337e-06
27  NWY  2006-10-16            0.004726        3.099954e-03
28  TEF  2002-02-08            0.010447        5.958070e-03
29  TEF  2002-02-11            0.009764        8.375140e-03
30  CIB  2006-08-18            0.001899        6.670807e-07
31  CIB  2006-08-21            0.001459        8.779171e-09
32  CIB  2006-08-22            0.004307        1.318464e-08
33  CIB  2006-08-23            0.006848        4.271603e-07
34  SKO  2002-02-08            0.059888        4.294716e-02
35  SKO  2002-02-11            0.061167        4.417510e-02
36  SKO  2002-02-12            0.061014        4.901067e-02
37  SKO  2002-02-13            0.055221        4.730380e-02
38  SKO  2002-02-14            0.061628        4.659908e-02
39  PAG  2007-07-03            0.005586        3.715073e-08
40  PAG  2007-07-05            0.008058        1.047600e-06
41  PAG  2007-07-06            0.007521        5.312208e-07
42  PAG  2007-07-09            0.007519        4.822871e-07
43  PAG  2007-07-10            0.006269        7.045978e-07
44  RBK  2002-02-08            0.119141        1.042945e-01
45  RBK  2002-02-11            0.128607        1.035408e-01
46  RBK  2002-02-12            0.131435        1.201102e-01
47  WGO  2002-02-08            0.109837        9.434335e-02
48  WGO  2002-02-11            0.094459        9.186975e-02
49  WGO  2002-02-12            0.109614        8.576695e-02
50  WGO  2002-02-13            0.110616        1.103984e-01
51  WGO  2002-02-14            0.116418        1.109057e-01
52  WAG  2002-02-08            0.059161        6.123514e-02
53  WAG  2002-02-11            0.067877        7.072952e-02
54  WAG  2002-02-12            0.073040        7.199622e-02
55  WAG  2002-02-13            0.060819        5.949971e-02

The situation is very similar to the great breakthrough of Black, Scholes and Merton whose model had a constant volatility assumption which everyone knew was not correct and did not hold in the sense that our alpha parameter is in theory constant per stock but the estimated alpha from last trade volatility surface is not constant.  A possibility that I might explore later is a third stochastic process for alpha but for now we have a clear model that is closed form, almost as fast as Heston model, and that improves the fit of Heston model overwhelmingly often (using last trades and not using bid-ask averages of option prices).
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Subject: ZULF MODEL FITS LAST TRADE VOLATILITY SURFACE BETTER THAN HESTON
MODEL IN MORE THAN 90% IN 56 CASES
From: "zulfikar.ahmed@gmail.com" <zulfikar.ahmed@gmail.com>
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———- Forwarded message ———-
From: “zulfikar.ahmed@gmail.com” <zulfikar.ahmed@gmail.com>
To: <jfrenkel@fma.if.usp.br>, <jhansen@uchicago.edu>, <jharrington@uchicago.edu>, <jharris@andrew.cmu.edu>, <jhp@uchicago.edu>, <jhricko_4@juno.com>, <jhs@math.ubc.ca>, <jhutasoi@andrew.cmu.edu>, <jianjunp@andrew.cmu.edu>, <jinha@uchicago.edu>, <jjbrehm@uchicago.edu>, <jlind@andrew.cmu.edu>, <jlondon@uchicago.edu>, <jlw@jhu.edu>, <jmateo@uchicago.edu>, <jmerseth@uchicago.edu>, <jmetcalf@ucsc.edu>, <jmg@uchicago.edu>, <jmogel@ucsc.edu>, <joel@scipp.ucsc.edu>, <joelms@andrew.cmu.edu>, <john.aldrich@vch.ca>, <john.beatty@interchange.ubc.ca>, <johncrawford53@hotmail.com>, <jose.oliveira@dfn.if.usp.br>, <josesoto@uem.mz>, <josue@fma.if.usp.br>, <jpadgett@uchicago.edu>, <jpbalz@uchicago.edu>, <jperuma1@jhu.edu>, <jpino@andrew.cmu.edu>, <jpitts@uchicago.edu>, <jpl@stat.cmu.edu>, <jpmccorm@uchicago.edu>, <jr67@andrew.cmu.edu>, <jrsteinb@illinois.edu>, <js5m@andrew.cmu.edu>, <js6n@andrew.cmu.edu>, <jsamuels@ucsc.edu>, <jthome@andrew.cmu.edu>, <julia_krause13@hotmail.com>, <jzal@phas.ubc.ca>, 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<s-ebelsduggan@northwestern.edu>, <safaa.bashir@guc.edu.eg>, <salladin7@aol.com>, <sanchita@gmail.com>, Shelley Anna <sanna@andrew.cmu.edu>, <sara@cmu.edu>, <savitt@interchange.ubc.ca>, <sbatiuk1@jhu.edu>, <sbchavel@uchicago.edu>, <russ@cmphys.phys.cmu.edu>, <sberrym@interchange.ubc.ca>, <sbevel@uchicago.edu>, <scheines@cmu.edu>, <schneider@cmu.edu>, <schoetzau@math.ubc.ca>, <schonbek@ucsc.edu>, <schulten@illinois.edu>, <schumacher@ernest.phys.cmu.edu>, <scoopbd@gmail.com>, <sdasgup2@ucsc.edu>, <sef@cs.cmu.edu>, <sej@uchicago.edu>, <selvin@illinois.edu>, <sendsen@cmu.edu>, <serrede@illinois.edu>, <sethmayer2014@northwestern.edu>, <sev@uchicago.edu>, <sfenner@uchicago.edu>, <sfli@andrew.cmu.edu>, <sg23@andrew.cmu.edu>, <sgalloway@uchicago.edu>, <sgm@uchicago.edu>, <sgraul@andrew.cmu.edu>, <sgross11@jhu.edu>, <shlomo@andrew.cmu.edu>, David Shwayder <shwayder@illinois.edu>, <sieg@cmu.edu>, <simchen@interchange.ubc.ca>, <simons@andrew.cmu.edu>, <sisotani@fge.if.usp.br>, <skoplik1@jhu.edu>, <slade@math.ubc.ca>, <slamb@illinois.edu>, <slater@uchicago.edu>, <slcooper@illinois.edu>, james P <strivergreen@gmail.com>, <bm@falconfone.com>
Cc:
Date: Tue, 22 Mar 2016 11:09:16 -0700
Subject: ZULF MODEL FITS LAST TRADE VOLATILITY SURFACE BETTER THAN HESTON MODEL IN MORE THAN 90% IN 56 CASES

I am pleased to announce that our time-fractional Heston model fits the volatility surfaces determined by the LAST TRADE of call options statistically significantly better than the Heston model in 51/55 of the cases (stock/day) that I have checked last night.  The model differs from the Heston model by a single extra parameter 0<alpha<2.  The comparison is to calibrate both the Heston and Zulf models on a volatility surface and record the error of fit (sum of absolute difference of implied volatilities). The paired t-test of these errors give:

>>> ttest_rel(x.ix[:,2],x.ix[:,3])
(array(4.27139160907284), 7.7558339944524236e-05)

Here is the actual table of errors

UPL  2003-01-02  0.0957002682349182  0.0773492111916326
0   UPL  2003-01-03            0.078657        6.652813e-02
1   UPL  2003-01-06            0.069270        5.893240e-02
2   KMI  2002-02-08            0.007780        6.266435e-03
3   KMI  2002-02-11            0.008966        5.994275e-03
4   KMI  2002-02-12            0.008309        5.424351e-03
5   KMI  2002-02-13            0.007713        5.128947e-03
6   KMI  2002-02-14            0.005948        5.272464e-03
7   PAC  2006-11-21            0.000290        1.745138e-07
8   PAC  2006-11-22            0.000558        3.908786e-07
9   NFG  2003-01-02            0.088293        8.326848e-02
10  NFG  2003-01-03            0.092200        1.840495e-02
11  NFG  2003-01-06            0.082446        6.947264e-02
12  NFG  2003-01-07            0.089481        1.946255e-02
13  NFG  2003-01-08            0.091463        8.470383e-02
14  OXY  2002-02-08            0.034763        3.187211e-02
15  OXY  2002-02-11            0.029676        3.690711e-02
16  OXY  2002-02-12            0.022510        1.772629e-02
17  OXY  2002-02-13            0.017657        2.116841e-02
18  OXY  2002-02-14            0.024343        3.202859e-02
19  AEM  2002-02-08            0.123033        1.217102e-01
20  AEM  2002-02-11            0.110734        6.377745e-02
21  AEM  2002-02-12            0.100758        9.943284e-02
22  AEM  2002-02-13            0.088986        8.803400e-02
23  AEM  2002-02-14            0.103508        9.958264e-02
24  NWY  2006-10-11            0.005319        4.450291e-08
25  NWY  2006-10-12            0.001743        1.144806e-07
26  NWY  2006-10-13            0.004078        2.571337e-06
27  NWY  2006-10-16            0.004726        3.099954e-03
28  TEF  2002-02-08            0.010447        5.958070e-03
29  TEF  2002-02-11            0.009764        8.375140e-03
30  CIB  2006-08-18            0.001899        6.670807e-07
31  CIB  2006-08-21            0.001459        8.779171e-09
32  CIB  2006-08-22            0.004307        1.318464e-08
33  CIB  2006-08-23            0.006848        4.271603e-07
34  SKO  2002-02-08            0.059888        4.294716e-02
35  SKO  2002-02-11            0.061167        4.417510e-02
36  SKO  2002-02-12            0.061014        4.901067e-02
37  SKO  2002-02-13            0.055221        4.730380e-02
38  SKO  2002-02-14            0.061628        4.659908e-02
39  PAG  2007-07-03            0.005586        3.715073e-08
40  PAG  2007-07-05            0.008058        1.047600e-06
41  PAG  2007-07-06            0.007521        5.312208e-07
42  PAG  2007-07-09            0.007519        4.822871e-07
43  PAG  2007-07-10            0.006269        7.045978e-07
44  RBK  2002-02-08            0.119141        1.042945e-01
45  RBK  2002-02-11            0.128607        1.035408e-01
46  RBK  2002-02-12            0.131435        1.201102e-01
47  WGO  2002-02-08            0.109837        9.434335e-02
48  WGO  2002-02-11            0.094459        9.186975e-02
49  WGO  2002-02-12            0.109614        8.576695e-02
50  WGO  2002-02-13            0.110616        1.103984e-01
51  WGO  2002-02-14            0.116418        1.109057e-01
52  WAG  2002-02-08            0.059161        6.123514e-02
53  WAG  2002-02-11            0.067877        7.072952e-02
54  WAG  2002-02-12            0.073040        7.199622e-02
55  WAG  2002-02-13            0.060819        5.949971e-02

The situation is very similar to the great breakthrough of Black, Scholes and Merton whose model had a constant volatility assumption which everyone knew was not correct and did not hold in the sense that our alpha parameter is in theory constant per stock but the estimated alpha from last trade volatility surface is not constant.  A possibility that I might explore later is a third stochastic process for alpha but for now we have a clear model that is closed form, almost as fast as Heston model, and that improves the fit of Heston model overwhelmingly often (using last trades and not using bid-ask averages of option prices).
3 Attachments

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Message-ID: <CAOKUxJBApka+wV4-R2nY6UkNdDF36=nFw7otMYBTodK=XB1+zQ@mail.gmail.com>
Subject: ZULF MODEL FITS LAST TRADE VOLATILITY SURFACE BETTER THAN HESTON
MODEL IN MORE THAN 90% IN 56 CASES
From: “zulfikar.ahmed@gmail.com” <zulfikar.ahmed@gmail.com>

slcooper@illinois.edu, james P <strivergreen@gmail.com>, bm@falconfone.com
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Date: Tue, 22 Mar 2016 11:09:16 -0700
Subject: ZULF MODEL FITS LAST TRADE VOLATILITY SURFACE BETTER THAN HESTON MODEL IN MORE THAN 90% IN 56 CASES

I am pleased to announce that our time-fractional Heston model fits the volatility surfaces determined by the LAST TRADE of call options statistically significantly better than the Heston model in 51/55 of the cases (stock/day) that I have checked last night.  The model differs from the Heston model by a single extra parameter 0<alpha<2.  The comparison is to calibrate both the Heston and Zulf models on a volatility surface and record the error of fit (sum of absolute difference of implied volatilities). The paired t-test of these errors give:

>>> ttest_rel(x.ix[:,2],x.ix[:,3])
(array(4.27139160907284), 7.7558339944524236e-05)

Here is the actual table of errors

UPL  2003-01-02  0.0957002682349182  0.0773492111916326
0   UPL  2003-01-03            0.078657        6.652813e-02
1   UPL  2003-01-06            0.069270        5.893240e-02
2   KMI  2002-02-08            0.007780        6.266435e-03
3   KMI  2002-02-11            0.008966        5.994275e-03
4   KMI  2002-02-12            0.008309        5.424351e-03
5   KMI  2002-02-13            0.007713        5.128947e-03
6   KMI  2002-02-14            0.005948        5.272464e-03
7   PAC  2006-11-21            0.000290        1.745138e-07
8   PAC  2006-11-22            0.000558        3.908786e-07
9   NFG  2003-01-02            0.088293        8.326848e-02
10  NFG  2003-01-03            0.092200        1.840495e-02
11  NFG  2003-01-06            0.082446        6.947264e-02
12  NFG  2003-01-07            0.089481        1.946255e-02
13  NFG  2003-01-08            0.091463        8.470383e-02
14  OXY  2002-02-08            0.034763        3.187211e-02
15  OXY  2002-02-11            0.029676        3.690711e-02
16  OXY  2002-02-12            0.022510        1.772629e-02
17  OXY  2002-02-13            0.017657        2.116841e-02
18  OXY  2002-02-14            0.024343        3.202859e-02
19  AEM  2002-02-08            0.123033        1.217102e-01
20  AEM  2002-02-11            0.110734        6.377745e-02
21  AEM  2002-02-12            0.100758        9.943284e-02
22  AEM  2002-02-13            0.088986        8.803400e-02
23  AEM  2002-02-14            0.103508        9.958264e-02
24  NWY  2006-10-11            0.005319        4.450291e-08
25  NWY  2006-10-12            0.001743        1.144806e-07
26  NWY  2006-10-13            0.004078        2.571337e-06
27  NWY  2006-10-16            0.004726        3.099954e-03
28  TEF  2002-02-08            0.010447        5.958070e-03
29  TEF  2002-02-11            0.009764        8.375140e-03
30  CIB  2006-08-18            0.001899        6.670807e-07
31  CIB  2006-08-21            0.001459        8.779171e-09
32  CIB  2006-08-22            0.004307        1.318464e-08
33  CIB  2006-08-23            0.006848        4.271603e-07
34  SKO  2002-02-08            0.059888        4.294716e-02
35  SKO  2002-02-11            0.061167        4.417510e-02
36  SKO  2002-02-12            0.061014        4.901067e-02
37  SKO  2002-02-13            0.055221        4.730380e-02
38  SKO  2002-02-14            0.061628        4.659908e-02
39  PAG  2007-07-03            0.005586        3.715073e-08
40  PAG  2007-07-05            0.008058        1.047600e-06
41  PAG  2007-07-06            0.007521        5.312208e-07
42  PAG  2007-07-09            0.007519        4.822871e-07
43  PAG  2007-07-10            0.006269        7.045978e-07
44  RBK  2002-02-08            0.119141        1.042945e-01
45  RBK  2002-02-11            0.128607        1.035408e-01
46  RBK  2002-02-12            0.131435        1.201102e-01
47  WGO  2002-02-08            0.109837        9.434335e-02
48  WGO  2002-02-11            0.094459        9.186975e-02
49  WGO  2002-02-12            0.109614        8.576695e-02
50  WGO  2002-02-13            0.110616        1.103984e-01
51  WGO  2002-02-14            0.116418        1.109057e-01
52  WAG  2002-02-08            0.059161        6.123514e-02
53  WAG  2002-02-11            0.067877        7.072952e-02
54  WAG  2002-02-12            0.073040        7.199622e-02
55  WAG  2002-02-13            0.060819        5.949971e-02

The situation is very similar to the great breakthrough of Black, Scholes and Merton whose model had a constant volatility assumption which everyone knew was not correct and did not hold in the sense that our alpha parameter is in theory constant per stock but the estimated alpha from last trade volatility surface is not constant.  A possibility that I might explore later is a third stochastic process for alpha but for now we have a clear model that is closed form, almost as fast as Heston model, and that improves the fit of Heston model overwhelmingly often (using last trades and not using bid-ask averages of option prices).
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Subject: ZULF MODEL FITS LAST TRADE VOLATILITY SURFACE BETTER THAN HESTON
MODEL IN MORE THAN 90% IN 56 CASES
From: "zulfikar.ahmed@gmail.com" <zulfikar.ahmed@gmail.com>
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Cc:
Date: Tue, 22 Mar 2016 11:09:16 -0700
Subject: ZULF MODEL FITS LAST TRADE VOLATILITY SURFACE BETTER THAN HESTON MODEL IN MORE THAN 90% IN 56 CASES

I am pleased to announce that our time-fractional Heston model fits the volatility surfaces determined by the LAST TRADE of call options statistically significantly better than the Heston model in 51/55 of the cases (stock/day) that I have checked last night.  The model differs from the Heston model by a single extra parameter 0<alpha<2.  The comparison is to calibrate both the Heston and Zulf models on a volatility surface and record the error of fit (sum of absolute difference of implied volatilities). The paired t-test of these errors give:

>>> ttest_rel(x.ix[:,2],x.ix[:,3])
(array(4.27139160907284), 7.7558339944524236e-05)

Here is the actual table of errors

UPL  2003-01-02  0.0957002682349182  0.0773492111916326
0   UPL  2003-01-03            0.078657        6.652813e-02
1   UPL  2003-01-06            0.069270        5.893240e-02
2   KMI  2002-02-08            0.007780        6.266435e-03
3   KMI  2002-02-11            0.008966        5.994275e-03
4   KMI  2002-02-12            0.008309        5.424351e-03
5   KMI  2002-02-13            0.007713        5.128947e-03
6   KMI  2002-02-14            0.005948        5.272464e-03
7   PAC  2006-11-21            0.000290        1.745138e-07
8   PAC  2006-11-22            0.000558        3.908786e-07
9   NFG  2003-01-02            0.088293        8.326848e-02
10  NFG  2003-01-03            0.092200        1.840495e-02
11  NFG  2003-01-06            0.082446        6.947264e-02
12  NFG  2003-01-07            0.089481        1.946255e-02
13  NFG  2003-01-08            0.091463        8.470383e-02
14  OXY  2002-02-08            0.034763        3.187211e-02
15  OXY  2002-02-11            0.029676        3.690711e-02
16  OXY  2002-02-12            0.022510        1.772629e-02
17  OXY  2002-02-13            0.017657        2.116841e-02
18  OXY  2002-02-14            0.024343        3.202859e-02
19  AEM  2002-02-08            0.123033        1.217102e-01
20  AEM  2002-02-11            0.110734        6.377745e-02
21  AEM  2002-02-12            0.100758        9.943284e-02
22  AEM  2002-02-13            0.088986        8.803400e-02
23  AEM  2002-02-14            0.103508        9.958264e-02
24  NWY  2006-10-11            0.005319        4.450291e-08
25  NWY  2006-10-12            0.001743        1.144806e-07
26  NWY  2006-10-13            0.004078        2.571337e-06
27  NWY  2006-10-16            0.004726        3.099954e-03
28  TEF  2002-02-08            0.010447        5.958070e-03
29  TEF  2002-02-11            0.009764        8.375140e-03
30  CIB  2006-08-18            0.001899        6.670807e-07
31  CIB  2006-08-21            0.001459        8.779171e-09
32  CIB  2006-08-22            0.004307        1.318464e-08
33  CIB  2006-08-23            0.006848        4.271603e-07
34  SKO  2002-02-08            0.059888        4.294716e-02
35  SKO  2002-02-11            0.061167        4.417510e-02
36  SKO  2002-02-12            0.061014        4.901067e-02
37  SKO  2002-02-13            0.055221        4.730380e-02
38  SKO  2002-02-14            0.061628        4.659908e-02
39  PAG  2007-07-03            0.005586        3.715073e-08
40  PAG  2007-07-05            0.008058        1.047600e-06
41  PAG  2007-07-06            0.007521        5.312208e-07
42  PAG  2007-07-09            0.007519        4.822871e-07
43  PAG  2007-07-10            0.006269        7.045978e-07
44  RBK  2002-02-08            0.119141        1.042945e-01
45  RBK  2002-02-11            0.128607        1.035408e-01
46  RBK  2002-02-12            0.131435        1.201102e-01
47  WGO  2002-02-08            0.109837        9.434335e-02
48  WGO  2002-02-11            0.094459        9.186975e-02
49  WGO  2002-02-12            0.109614        8.576695e-02
50  WGO  2002-02-13            0.110616        1.103984e-01
51  WGO  2002-02-14            0.116418        1.109057e-01
52  WAG  2002-02-08            0.059161        6.123514e-02
53  WAG  2002-02-11            0.067877        7.072952e-02
54  WAG  2002-02-12            0.073040        7.199622e-02
55  WAG  2002-02-13            0.060819        5.949971e-02

The situation is very similar to the great breakthrough of Black, Scholes and Merton whose model had a constant volatility assumption which everyone knew was not correct and did not hold in the sense that our alpha parameter is in theory constant per stock but the estimated alpha from last trade volatility surface is not constant.  A possibility that I might explore later is a third stochastic process for alpha but for now we have a clear model that is closed form, almost as fast as Heston model, and that improves the fit of Heston model overwhelmingly often (using last trades and not using bid-ask averages of option prices).
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From: “zulfikar.ahmed@gmail.com” <zulfikar.ahmed@gmail.com>
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Cc:
Date: Tue, 22 Mar 2016 11:09:16 -0700
Subject: ZULF MODEL FITS LAST TRADE VOLATILITY SURFACE BETTER THAN HESTON MODEL IN MORE THAN 90% IN 56 CASES

I am pleased to announce that our time-fractional Heston model fits the volatility surfaces determined by the LAST TRADE of call options statistically significantly better than the Heston model in 51/55 of the cases (stock/day) that I have checked last night.  The model differs from the Heston model by a single extra parameter 0<alpha<2.  The comparison is to calibrate both the Heston and Zulf models on a volatility surface and record the error of fit (sum of absolute difference of implied volatilities). The paired t-test of these errors give:

>>> ttest_rel(x.ix[:,2],x.ix[:,3])
(array(4.27139160907284), 7.7558339944524236e-05)

Here is the actual table of errors

UPL  2003-01-02  0.0957002682349182  0.0773492111916326
0   UPL  2003-01-03            0.078657        6.652813e-02
1   UPL  2003-01-06            0.069270        5.893240e-02
2   KMI  2002-02-08            0.007780        6.266435e-03
3   KMI  2002-02-11            0.008966        5.994275e-03
4   KMI  2002-02-12            0.008309        5.424351e-03
5   KMI  2002-02-13            0.007713        5.128947e-03
6   KMI  2002-02-14            0.005948        5.272464e-03
7   PAC  2006-11-21            0.000290        1.745138e-07
8   PAC  2006-11-22            0.000558        3.908786e-07
9   NFG  2003-01-02            0.088293        8.326848e-02
10  NFG  2003-01-03            0.092200        1.840495e-02
11  NFG  2003-01-06            0.082446        6.947264e-02
12  NFG  2003-01-07            0.089481        1.946255e-02
13  NFG  2003-01-08            0.091463        8.470383e-02
14  OXY  2002-02-08            0.034763        3.187211e-02
15  OXY  2002-02-11            0.029676        3.690711e-02
16  OXY  2002-02-12            0.022510        1.772629e-02
17  OXY  2002-02-13            0.017657        2.116841e-02
18  OXY  2002-02-14            0.024343        3.202859e-02
19  AEM  2002-02-08            0.123033        1.217102e-01
20  AEM  2002-02-11            0.110734        6.377745e-02
21  AEM  2002-02-12            0.100758        9.943284e-02
22  AEM  2002-02-13            0.088986        8.803400e-02
23  AEM  2002-02-14            0.103508        9.958264e-02
24  NWY  2006-10-11            0.005319        4.450291e-08
25  NWY  2006-10-12            0.001743        1.144806e-07
26  NWY  2006-10-13            0.004078        2.571337e-06
27  NWY  2006-10-16            0.004726        3.099954e-03
28  TEF  2002-02-08            0.010447        5.958070e-03
29  TEF  2002-02-11            0.009764        8.375140e-03
30  CIB  2006-08-18            0.001899        6.670807e-07
31  CIB  2006-08-21            0.001459        8.779171e-09
32  CIB  2006-08-22            0.004307        1.318464e-08
33  CIB  2006-08-23            0.006848        4.271603e-07
34  SKO  2002-02-08            0.059888        4.294716e-02
35  SKO  2002-02-11            0.061167        4.417510e-02
36  SKO  2002-02-12            0.061014        4.901067e-02
37  SKO  2002-02-13            0.055221        4.730380e-02
38  SKO  2002-02-14            0.061628        4.659908e-02
39  PAG  2007-07-03            0.005586        3.715073e-08
40  PAG  2007-07-05            0.008058        1.047600e-06
41  PAG  2007-07-06            0.007521        5.312208e-07
42  PAG  2007-07-09            0.007519        4.822871e-07
43  PAG  2007-07-10            0.006269        7.045978e-07
44  RBK  2002-02-08            0.119141        1.042945e-01
45  RBK  2002-02-11            0.128607        1.035408e-01
46  RBK  2002-02-12            0.131435        1.201102e-01
47  WGO  2002-02-08            0.109837        9.434335e-02
48  WGO  2002-02-11            0.094459        9.186975e-02
49  WGO  2002-02-12            0.109614        8.576695e-02
50  WGO  2002-02-13            0.110616        1.103984e-01
51  WGO  2002-02-14            0.116418        1.109057e-01
52  WAG  2002-02-08            0.059161        6.123514e-02
53  WAG  2002-02-11            0.067877        7.072952e-02
54  WAG  2002-02-12            0.073040        7.199622e-02
55  WAG  2002-02-13            0.060819        5.949971e-02

The situation is very similar to the great breakthrough of Black, Scholes and Merton whose model had a constant volatility assumption which everyone knew was not correct and did not hold in the sense that our alpha parameter is in theory constant per stock but the estimated alpha from last trade volatility surface is not constant.  A possibility that I might explore later is a third stochastic process for alpha but for now we have a clear model that is closed form, almost as fast as Heston model, and that improves the fit of Heston model overwhelmingly often (using last trades and not using bid-ask averages of option prices).
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