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Matlab Code for Density of Stochastic Differential Equations with Stochastic Calculus of Standard Deviations

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 Ahsan Amin, CEO at Infiniti Derivatives Technologies

 Thursday, January 29, 2015

I have written this initial experimental demonstration program to find the density of stochastic differential equation dX(t)=mT1 * X(t)^pT1 *dt + epsilon * X(t)^pV * dz(t) We also find the density of integral dI(t)=mT3.*X(t)^pT3 *dt. We find the second moment locally along standard deviations of SDE The second moment equation is d[X(t)^2]=mT1.*2.*X(t)^(1+pT1)*dt+2*epsilon*X(t)^(1+pV)*dz(t)+epsilon^2*X(t)^(2*pV)*dt; The program works extremely well for most cases. In order to have an idea about how good the approximation is, I have also added a monte carlo density generation program. Since the steps are extremely short, monte carlo gives quite good results and a perfectly valid comparison can be made in 98% of cases. . The larger plan is to find conditional values of time integrals of stochastic processes for shorter time spans using the above method (SCSD) and then use them with Girsanov and transition probabilities framework to simulate density of a stochastic differential equation and density of its functions/moments for large time horizons with great precision. I will soon be releasing another program that would map these time integrals from standard deviation grid to a fixed grid that can be used directly for simulation of SDEs and functions of SDE using transition probabilities framework. Here you can go to the link to download the program. http://www.wilmott.com/messageview.cfm?catid=4&threadid=98049


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1 comments on article "Matlab Code for Density of Stochastic Differential Equations with Stochastic Calculus of Standard Deviations"

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 RAFAEL MARTINEZ MUNOZ, Adjunct Professor at Miami Dade College

 Saturday, January 31, 2015



Great add to Matlab. Would allow derivative and options model simulation for OPM..

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