Archive for May, 2017

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

Attachments5:09 AM (2 hours ago)
to harrington, jharris, jhp, jhricko_4, jianjunp, jinha, jjbrehm, jlind, jlondon, jlw, jmateo, jmerseth, jmetcalf, jmg, jmogel, joel, joelms, john.aldrich, john.beatty, johncrawford53, jose.oliveira, josesoto, josue, jpadgett, jpbalz

​Ladie​s and Gentlemen,

I was introduced to the issue of long memory at Gresham Investment Management where Benoit Mandelbrot had advised the principals; this was around a decade ago.  It took me a decade to understand what long memory in option prices means concretely to produce closed form stochastic volatility models from these extending Heston/Bates and the affine models.  Research papers on the topic goes back to 2000-2005 but a concrete closed form model that actually outperforms affine type models with jumps in price and volatility was new.  We are now looking into the issue of whether these models are able to consistently and universally make profits from mispricings of the market makers in liquid options.  This is not a hard problem if one wants to produce a trading strategy for a single option by hammering together something reasonable.  It is a hard problem if one wants to produce a system that is able to profit against the market makers’ mispricing universally.

To this end, I have produced a system that can produce tradeable strategies with a few tunable parameters.  The idea of the strategies is the combination of a VOLATILITY/VOLATILITY SURFACE PREDICTION with an ARBITRAGE OF MARKET MAKER MISPRICING.

One can use arbitrarily sophisticated methods for volatility and volatility surface prediction.  I use an ARFIMA model to predict the log(return^2) volatility of the underlying and a LASSO prediction of the multivariate time series of the 9 parameters of the Zulf SV model.  The LASSO model does not croak when the lookback period is small which is the reason I use it rather than a basic non-regularized linear model; empirically I found that an 80/20 mix of historical average of parameters and LASSO prediction produces better forecasts.  This part is not particularly optimal but it is not the central problem.

More important is the problem of the understanding what is the PRICE THRESHOLD of mispricing.  Here we have results that are far more nontrivial:  we find that the ERROR OF FITTING VOLATILITY SURFACES is the key part of the price threshold we should use.  So the objective function used to fit the volatility surfaces is sqrt(sum(ModelCallPx-MarketCallPx)^2/N) which is the average dollar mispricing per surface.  The best surface fits produces a minimal error of this type which we then use to decide the mispricing level.  This mispricing level seems to be central to actually systematically profiting from the option markets despite a big bid-ask spread!

Let me repeat this a few times so this is clear.  The POWER of the ZULF STOCHASTIC VOLATILITY model is not just that it fits the call prices better than other popular models (like Bates which is better than Heston adding jumps to prices and volatility) but that for 2015 for some of the liquid options the ERROR OF FIT can be used to define nontrivial MISPRICING THRESHOLDS with systematic good performance despite wide bid-ask spreads.  Let’s take a look at some graphs without any stop losses to appreciate the importance of this result.

Inline image 1

Inline image 4

Ok these graphs may not look pretty but they have no stoplosses or other artificial smoothing.  Now I know from a great deal of experience that it is not hard to produce strategies that are winners 65% of the times.  These are strategies with 80-90% winners (which is not as easy).

Both of these are produced by tuning the three parameters; the mispricing threshold is defined as CONST*ErrorOfVolSurfaceFit for the calibration of that day.  This is actually what produces the reasonable results above in backtests.  Second is a pair of VOLATILITY DIRECTION thresholds which essentially ensures that one does not short the option when the expected volatility is to rise.  This is also crucial:  we want to only do trades consistent with the volatility prediction.  Profitability of a volatility surface prediction strategy in these cases depends on making sure that one does not do ‘full delta hedging’ which means that they are not viable by shorting options when the volatility is expected to rise.

Finally, here is a harder example:  EEM where the results are not as clean but you can see that this problem of producing universal results is a tractable problem at least for 2015.
Inline image 3

Of course if I put in a stop loss these would look much  better but that’s not so useful because we want to understand what’s driving the profits; we want universal results over all liquid options because we believe that the Zulf SV model is the best option pricing model in the world and is much better than whatever the option market makers are doing.  My explanation for why this works is precisely because the ERROR OF FITS of the volatility surface is used as thresholds (modulo a constant in [1,5] say).  In fact you can play around with fixed constant thresholds which is what I did till I realized the above and find that the results are much less steady.  On the problematic side, the universality I would like to see does not come without tuning the constants for each stock.

The code attached shows you the details of what produces these results — the valuation code is in cmlf.pyx and the details of the arbitrage strategy in predVSParamsStrategy.R.

I would like to propose to the world that:  STOCHASTIC VOLATILITY MODELS formalized is a SOLVED PROBLEM.  A hard nontrivial problem is the problem of optimal implementation of stochastic volatility models to somehow force arbitrage-freeness.  In other words thus far, this problem has been in the domain of PRACTICE while in fact, this seems to me to be as nontrivial a theoretical issue as the SV models themselves.  Who knows?  Maybe this is the equivalent of Google’s search engine problem ….
The attached files besides some of the code (for which you will need actual historical options data though) as well as files marked *-ret.txt which are extracted returns, *-vsps.txt which is the detailed output of the volatility surface prediction strategy that used PRECALIBRATED ZULF MODEL parameters all in the fill All-calibrations.txt.  But you can examine the takeArbitragePositions and other functions in the R code to verify that these are serious strategies.
11 Attachments

Read Full Post »


Hep bored bark heater corker
Pick beck barker borker cussed
Linger worker sinder barser sorter marker
Chalker marker heeker corker power sir door dear cock goyer
Park here seer we tear mark parker work porker part here
Soop west perk cock gem garker where bured here sure sister
Mark west here heart dock we are foyer where God cork
Cull cark kem poom bum pyre we’re four pin higher guyer
Carker coker muck bare shit goyer part entire erty heart
Boyer pierce here shit gayer bark he is here coyer seer
More sim said here gored heart heart higher sivo tader
Gold bare west empire we are coyer part here sir
Song song winner we are cold bet bark here sin
Air dirty here core seer mark here seer
We are furor heart hemmer wedder we are furor
Furor tum tum teb teb talk we are shoyer corker
Mark he sir soyer bet higher guyer poosier mored heart
Higher hewoter duck we are fure higher erder
Dock goyer part here part we are part air dirt here
Ust inned we are fureter ewo dirt guyer ewo pyre
Ewo torder birdy we are furor bayor bork pin
Est part part bored heart hut gook air barter mark he’s a coyer
Cold bedder mark fire here targer gone park here sister
Mored teck we are soyer pureder higher guyer fire pin
Parn parn pate put pull pooper park we are God heart
Go faster marn colder cart darker mark here seer
Joker poker we are fierced ear sick bare goyer pun
Hewest art cure mark park wait here cold pet pure fire
Work park bored here bored hearter bored parker
Bored pyre ford a dirt here cold pen work air doored here
Denned winner fork kin why sipper we were foyer
Cull pin ark bed head ark empire we are hair part
Hoter God empire wit here hen ire shit cure cure pair
God guard talk work sing ark choker messed lear
Fairst talk wang guard here toker hearter ert dock dock
West pin fire hero tear park ewest ear doored we are cold
Bark park hark deck doyer pyre fair shit keer dock we are
Cold fire hoyer God cart hide cureder dock we are wedder tear
Cord dead dire goyer pin ark God higher bard dock God hearter
God poop foyer sire soyer poyer God buyer ewest here
Bark bare look hooter dark here sung we are tork kin
Bark pin fire higher guider hider booer seer chooter
Men park here erst farter weaker bin bark pure sit dire
Air bard we are west here seer choker moo fooer work bare
Work whoer park pure work fire singer dick dire joer part nen
Dark heater dark haker mark fure sim sio power
Seer we are toyer coyer fire beg buyer work we are cord deb
Weak fire weak higher dick dare weak pure fure seer
Log chire mark here sing we are talker foyer mark lick
Joder bore singer we are colder bore bore pure
Bore part bore foyer bore heart bore guard bore fire
Bore pooper bore whered bore part bore part bore hotter
Bore toter bore porter bore lowester bore porker bore part
Bore foyer bore coyer bore soyer bore toyer bore doyer
Bore doyer bore shoyer bore towarder den dark
Bore toyer bore toyer boyer hoyer bore toyer bore coyer
Bore shoyer bore doyer bore tire bore soyer bore air mard
Bore dogger bore tarker bore shorter bore dirter
Bore corter bore sorter bore shoyer art kit
Bore tire sir bore shister bore tart bore dark bore shin
Bore cart bore shin bore guard bore tuck bore shin
Bore cart bore hin bore deck bore buck bore puck bore pin
Bore fart bore bust bore part bore fen bore log
Bore forced bore coarsed bore fest bore fark bore pin
Bore parker bore fin bore farker bore fester bore wick
Bore pick bore pin bore fist bore win bore pure bore cure
Bore furester bore work bore poor bore bared bore cure dirt here
Bore pisser bore pitter bore fister bore Godder bore teng
Bore foyer bore fire bore carker bore fureter bore part
Bore pest bore fured bore west bore pair bore heo bore park
Bore dared bore pyre art here bore bart bore part bore buyer
Bore bart bore cooker bore part bore dog bore work
Bore fure bore dog bore leng bore tark bore we are fierceter
Oured bore pure bore ping bore deck bore deck bore dark
Bore deck bore deck we are feared here bore bare bore bard
Bore talk bore we are bore pure bore bore bore part
Bore shit bore dark bore deck bore dark bore deck bore
Bore teng whered here bore bark bore part ewo tear bore we are feared here
Bore deg bore deng bore teng bore deng bore bared heart
Bore dare bore tire bore bard bore pure bore poor bore fork
Bore pin bore entire bore dare bore pooper bore we are bore sork
Bore noyer bore poor west tick we are we are bore
Bore wah bore park bore pen we are bore pure
Bore tart whered best cure are we deared here?
Bore benia bore bared bore bore bore taig bore dock
Wid bore dog bore duck bore bark bore look bore teng
Bore kick bore den bore dire bore sark bore deck
Bore we are west bore dire bore looer harked bore lick
West here dear bore weirder bore deader bore winner
Bore ninner bore pureter bore fure sir bore loo core
Bore nist nayer bore dead higher bore bed art
Bored head dark heo sio we’re west bork en cart dare Iowa tick
IOWA we were seer hemmer we are bore

Read Full Post »