SERVING THE QUANTITATIVE FINANCE COMMUNITY

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by Amin
Yesterday, 4:17 pm
Forum: Off Topic
Topic: How to safeguard my research
Replies: 983
Views: 72324

Re: How to safeguard my research

I have been writing on this thread for many many long years. And there is a long story of disgusting treatment, torture and persecution here. CIA kept track of the people reading on my thread and while I used to write the stories of torture, they allowed me to write everything with great hubris and ...
by Amin
December 14th, 2019, 4:07 pm
Forum: Technical Forum
Topic: Breakthrough in the theory of stochastic differential equations and their simulation
Replies: 839
Views: 79472

Re: Breakthrough in the theory of stochastic differential equations and their simulation

Here are the dependencies functions of the above program. function [ptCorrected] = CorrectProbAndMean(TrueMean,c1N,c2N,yy,pt,Pn)        %  u0=theta+(yy(mm)-theta)*exp(-kappa*(dt)); %analytic mean of the density %         %If you are not using stochastic volatility, replace above with %         %true...
by Amin
December 14th, 2019, 3:38 pm
Forum: Technical Forum
Topic: Breakthrough in the theory of stochastic differential equations and their simulation
Replies: 839
Views: 79472

Re: Breakthrough in the theory of stochastic differential equations and their simulation

In this program, I am simulating the SDE given as dyy(t)=mu1 yy(t)^beta1 dt + mu2 yy(t)^beta2 dt +sigma yy(t)^gamma dz(t) I have not directly simulated the SDE but simulated the transformed   Bessel process version of the SDE . There is one caveat as I used the process for fast mean reverting SDEs a...
by Amin
December 12th, 2019, 6:03 pm
Forum: Technical Forum
Topic: Breakthrough in the theory of stochastic differential equations and their simulation
Replies: 839
Views: 79472

Re: Breakthrough in the theory of stochastic differential equations and their simulation

OK friends, I wrote a different program for solution of densities of 1D SDEs. I took a fixed grid with 700 cells and pre-calculated transition probabilities and then evolved the SDE. This way you can almost solve for the density of any SDE. zero remains a minor problem but I will fix that. This grid...
by Amin
December 9th, 2019, 11:29 am
Forum: Technical Forum
Topic: Breakthrough in the theory of stochastic differential equations and their simulation
Replies: 839
Views: 79472

Re: Breakthrough in the theory of stochastic differential equations and their simulation

Friends sorry for the delay. But before we can precisely calculate two dimensional density in a stochastic volatility framework, we have to first write the program for precise calculation of dt-integrals and dz-integrals from the SDE evolution. I had earlier presented the idea of Ito-calculus on the...
by Amin
December 5th, 2019, 2:26 pm
Forum: Technical Forum
Topic: Breakthrough in the theory of stochastic differential equations and their simulation
Replies: 839
Views: 79472

Re: Breakthrough in the theory of stochastic differential equations and their simulation

I have written a program for two dimensional correlated stochastic volatility models in my framework which I used for 1D Lamperti transformed SDEs. I am testing the code and comparing it with two dimensional monte carlo. I hope to post a full-fledged and very general stochastic volatility pricing pr...
by Amin
November 27th, 2019, 4:32 pm
Forum: Technical Forum
Topic: Breakthrough in the theory of stochastic differential equations and their simulation
Replies: 839
Views: 79472

Re: Breakthrough in the theory of stochastic differential equations and their simulation

I am attaching the program for solution of SDEs in bessel or Lamperti transformed coordinates based on finite differences. This program in the original form becomes unstable after 8-12 time steps because finite differences on the boundary become unstable. Otherwise the program works fine and is ver...
by Amin
November 26th, 2019, 7:25 am
Forum: Technical Forum
Topic: Breakthrough in the theory of stochastic differential equations and their simulation
Replies: 839
Views: 79472

Re: Breakthrough in the theory of stochastic differential equations and their simulation

Tomorrow I will be posting my experimental programs for friends after writing explanation with the code. The first program is based solely on finite differences but I was able to make ghost points outside the boundary for finite-difference derivatives. For ghost points, I took divided differences of...
by Amin
November 23rd, 2019, 8:05 pm
Forum: Technical Forum
Topic: Breakthrough in the theory of stochastic differential equations and their simulation
Replies: 839
Views: 79472

Re: Breakthrough in the theory of stochastic differential equations and their simulation

Thank you Cuch for the paper. Yes it is definitely related to my work and it was a good read. I will give a more detailed review later. I want to tell the friends about progress on my work towards the solution to Fokker-Planck equation. I keep the solution in a hermite form as following [$]X(Z)=a_0(...
by Amin
November 13th, 2019, 3:32 pm
Forum: Technical Forum
Topic: Breakthrough in the theory of stochastic differential equations and their simulation
Replies: 839
Views: 79472

Re: Breakthrough in the theory of stochastic differential equations and their simulation

I was able to improve my finite differences a little bit to continue them for seven to eight time intervals of  [$]\Delta t=.125/8[$] and then I tried all sort of extreme parameters at different values of SDE starting point very close to zero and close to one and several other places. I just played...
by Amin
November 8th, 2019, 11:21 am
Forum: Technical Forum
Topic: Breakthrough in the theory of stochastic differential equations and their simulation
Replies: 839
Views: 79472

Re: Breakthrough in the theory of stochastic differential equations and their simulation

Friends, my work has been going rather slowly and there were several days that I was totally unable to work. I tried to solve the equations first by finite differences but my finite difference derivatives break down after a few steps at the boundary even though I try one-sided derivatives of the sa...
by Amin
November 2nd, 2019, 12:41 pm
Forum: Technical Forum
Topic: Breakthrough in the theory of stochastic differential equations and their simulation
Replies: 839
Views: 79472

Re: Breakthrough in the theory of stochastic differential equations and their simulation

An informal update for time being The right evolution equation along the CDF lines incorporating the effect of first and second mode (1st and 2nd equation post 815) is given as [$] X(t+\Delta t)=X(t)+(B(t + \Delta t) -B(t))  {(\frac{\partial X}{\partial B})} + \mu(X) {\Delta t} -2 \sigma(X) \frac{\...
by Amin
October 29th, 2019, 11:43 am
Forum: Technical Forum
Topic: Breakthrough in the theory of stochastic differential equations and their simulation
Replies: 839
Views: 79472

Re: Breakthrough in the theory of stochastic differential equations and their simulation

Friends, first please apologize me for writing this post without numerically checking the results. I had some basic ideas today that I want to share with friends hence the reason for writing this post. When we are doing an evolution or simulation scheme for the SDEs, we take an estimate of drift ov...
by Amin
October 26th, 2019, 3:59 pm
Forum: Technical Forum
Topic: Breakthrough in the theory of stochastic differential equations and their simulation
Replies: 839
Views: 79472

Re: Breakthrough in the theory of stochastic differential equations and their simulation

In my previous post, I suggested to expand the SDE variable [$]X(t)[$] as a function of hermite polynomials of the brownain motion but then I realized that drift and other functions of X(t) are basically non-linear functions and they non-linearly affect various hermite polynomials in the hermite po...
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