
5:01 PM (0 minutes ago) 


Dear Professor Donoho,
For univariate series it is not difficult to show that the Ito density phi(s) can be empirically calculated by evaluating f(x)=x^2 for the Ito formula and estimating the density from the formula as a derivative in time since f”(x) = 2 and the last term is simply \int_0^t p(s) ds. It can be shown to be not quite a power law. So given this variation term we expect that the diffusion term that produces it lies with fundamental factors that affect the entire market since the observed density of the volatility correlation market graph (around 75% of the possible nchoose2=n(n1)/2 possible edges) and it perhaps possible to explain the diffusion term observed empirically on univariate volatility series using a Laplacian diffusion (super or sub) using this underlying space for example the modeling of all volatility shocks across 1900 stocks which is what led to the deviation from power law in the shock count distribution that was detectable in previously posted material. This will be the next push in order to ensure that we maximize chances of producing a solid scientific model of global financial volatility using fractional Partial Differential equations with some finer understanding of what is deterministic and what is stochastic, which is still an open question for me in detail, although philosophically Einstein had no problems with statistical mechanics which simply models deterministic phenomena via statistical idealizations because the intensity of interactions of the Brownian particle is high. If volatility is a global object, should it act like a deterministic quantitiy or a stochastic quantity? Now there is fractional TAYLOR expansion for appropriate function classes which suggest that it is not necessarily correct to assume that existence of an ITO DENSITY implies stochasticity either. But since there is a chance that Laplacian on the graph could help resolve this issue providing an explanatory source of volatility or partially, I will try to read through the attached recent doctoral thesis on Laplacian on graphs and their use in complex network theory.
Advertisements
Leave a Reply