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by Amin
February 21st, 2024, 8:00 am
Forum: Technical Forum
Topic: Breakthrough in the theory of stochastic differential equations and their simulation
Replies: 2261
Views: 438318

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

Friends, I went to drawing board again and tried to see if I can improve the basic regression algorithm. And it works far better now after improvement of the algorithm. In the earlier algorithm Zx is sorted with respect to the asset but in new algorithm Zx is sorted with respect to uncorrelated part...
by Amin
February 20th, 2024, 10:26 pm
Forum: Technical Forum
Topic: Breakthrough in the theory of stochastic differential equations and their simulation
Replies: 2261
Views: 438318

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

I think it might be of some help so I just decided to post the working program as such. . . function [bnm,aa] = CalculateConditionalProbabilitiesYtoXLinearRegression04IterB(Yin,Xin) %Yin argument translates to independent random variable Y %Xin argument translates to dependent variable X. %This func...
by Amin
February 20th, 2024, 10:05 pm
Forum: Technical Forum
Topic: Breakthrough in the theory of stochastic differential equations and their simulation
Replies: 2261
Views: 438318

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

Friends, option prices would be perfectly retrieved from the 2D density of asset if sum of Zy density in first column and sum of Zx density in first row is perfectly equal to 1D marginal density of the asset.  So once we are given first column of Zy density that we calculated from 1st order cross m...
by Amin
February 20th, 2024, 9:08 pm
Forum: Technical Forum
Topic: Breakthrough in the theory of stochastic differential equations and their simulation
Replies: 2261
Views: 438318

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

Friends, option prices would be perfectly retrieved from the 2D density of asset if sum of Zy density in first column and sum of Zx density in first row is perfectly equal to 1D marginal density of the asset.  So once we are given first column of Zy density that we calculated from 1st order cross mo...
by Amin
February 20th, 2024, 9:37 am
Forum: Technical Forum
Topic: Breakthrough in the theory of stochastic differential equations and their simulation
Replies: 2261
Views: 438318

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

Friends, I have made quite some progress but some quick notes I wanted to share.  If you exogenously fix first row and first column, please make sure that derivative of Z-series/Hermite Series on first row or first column does not switch signs. Whenever a derivative switches signs on these border ro...
by Amin
February 19th, 2024, 8:03 pm
Forum: Technical Forum
Topic: Breakthrough in the theory of stochastic differential equations and their simulation
Replies: 2261
Views: 438318

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

Friends, as we see several times in iterative optimization that fit to moments becomes better but the density becomes spiked or rough. I believe that the reason behind it is that conditions for smoothness of the density are violated. The derivatives of Zy terms and Zx terms (as a whole one line or o...
by Amin
February 19th, 2024, 1:04 pm
Forum: Technical Forum
Topic: Breakthrough in the theory of stochastic differential equations and their simulation
Replies: 2261
Views: 438318

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

Friends, I am posting a very preliminary version of the main function that optimizes. It has several errors. For many idisosyncratic cases, parameters, loops count, loops order and many other things have to be tweaked. I still have not done the part that perfectly fixes the first column and first ro...
by Amin
February 18th, 2024, 12:43 pm
Forum: Technical Forum
Topic: Breakthrough in the theory of stochastic differential equations and their simulation
Replies: 2261
Views: 438318

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

Friends, I noticed that after I removed the error in previous program, the graphs became less robust and there were all sorts of spikes and instabilities. I have been working to fix that. I have had enough success. But more work needs to be done. I am showing some graphs from both totally non-correl...
by Amin
February 17th, 2024, 10:36 am
Forum: Technical Forum
Topic: Breakthrough in the theory of stochastic differential equations and their simulation
Replies: 2261
Views: 438318

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

Friends, we still have to work on better optimization and also on how to divide the marginal density better into first row and first column (I did this just ad-hoc yet). But I am sure that we are fixing all problems and issues one by one. Option prices are still far from perfect for high correlation...
by Amin
February 17th, 2024, 10:18 am
Forum: Technical Forum
Topic: Breakthrough in the theory of stochastic differential equations and their simulation
Replies: 2261
Views: 438318

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

Friends, yes there was an error in backing out standardized version of 2D density of X. I have fixed the error and played somewhat with the program and have been able to get very close shapes to stochastic volatility models with high negative correlations. Here are a few comparison graphs for the pr...
by Amin
February 16th, 2024, 8:56 pm
Forum: Technical Forum
Topic: Breakthrough in the theory of stochastic differential equations and their simulation
Replies: 2261
Views: 438318

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

Friends, I tried the suggestion in previous post and found out that actually this was not the problem and the way I was calculating derivatives on the slices, it was probably right. However I think that the part  of my program where I reverse the standardization to get densities back in original for...
by Amin
February 15th, 2024, 8:04 am
Forum: Technical Forum
Topic: Breakthrough in the theory of stochastic differential equations and their simulation
Replies: 2261
Views: 438318

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

Friends, we were not working with correlation earlier and my intention was to get the model to work somewhere and then fix the errors. Now when we have to work with correlations, I think we have an error in our jacobian calculation as well. We do change probability density in two dimensions with res...
by Amin
February 14th, 2024, 2:05 pm
Forum: Technical Forum
Topic: Breakthrough in the theory of stochastic differential equations and their simulation
Replies: 2261
Views: 438318

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

Friends, I could not work yesterday at all. For past fifteen days since the last antipsychotic injection, I have been feeling that something is very wrong and I have remained very off. I have been trying to figure out what was the reason behind my feeling not so good at all. I stopped taking tea and...
by Amin
February 13th, 2024, 12:22 am
Forum: Technical Forum
Topic: Breakthrough in the theory of stochastic differential equations and their simulation
Replies: 2261
Views: 438318

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

Friends, I have been thinking about how to later our analytic set up when the two stochastic variables X and Y are correlated. I think I have some ideas and I decided to share them with friends.  We have two variables X and Y and we are given their marginal densities as [$]Y(Z_y)\, =\, ah_0 \, +\, a...
by Amin
February 12th, 2024, 10:47 am
Forum: Technical Forum
Topic: Breakthrough in the theory of stochastic differential equations and their simulation
Replies: 2261
Views: 438318

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

Friends, I noticed a mistake in programs uploaded in post # 2181 in function function [bnm,aa] = CalculateConditionalProbabilitiesYtoXLinearRegression02(Yin,Xin) and in post #2185, when specifying regression matrices, I have made this mistake, For fifth hermite polynomial, I have written (Zx(1:Ndata...