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June 25th, 2021, 2:34 am
Forum: Technical Forum
Topic: Breakthrough in the theory of stochastic differential equations and their simulation
Replies: 1193
Views: 157165

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

What I have suggested in previous post has been reviewed in slightly different mathematical framework especially by Dr. Marco Avellaneda in one of his papers on pairs trading. I have not read his paper for years but I think when I was brainstorming with pairs trading with klamn filtering, many of th...
June 24th, 2021, 11:00 am
Forum: Technical Forum
Topic: Breakthrough in the theory of stochastic differential equations and their simulation
Replies: 1193
Views: 157165

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

Friends, my current post is about market trading and it has to be seen in context of the following previous posts. https://forum.wilmott.com/viewtopic.php?f=4&t=99702&start=1140#p866202 https://forum.wilmott.com/viewtopic.php?f=4&t=99702&start=1140#p866241 https://forum.wilmott.com/v...
June 19th, 2021, 8:50 am
Forum: Technical Forum
Topic: Breakthrough in the theory of stochastic differential equations and their simulation
Replies: 1193
Views: 157165

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

$dX = \mu \, {X}^{\beta} \, \int_0^t ds +\, {X}^{\gamma} \, \sum_{n=1}^{N} \, \sigma_{1n} \, \int_0^t dZ_n(s)$ $+(\mu \, \beta {X}^{\beta-1} ) \, (\mu \, {X}^{\beta}) \, \int_0^t \int_0^s dv \, ds$ [\$]+(\mu \, \beta {X}^{\beta-1} ) \, ({X}^{\gamma} ) \, \sum_{n=1}^{N} \, \sigma_{1n}  \, \...
June 17th, 2021, 6:42 pm
Forum: Technical Forum
Topic: Breakthrough in the theory of stochastic differential equations and their simulation
Replies: 1193
Views: 157165

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

Friends, I wanted to share the analytics for multidimensional monte carlo simulations of the kind we have in equity basket pricing where each of the N SDEs in the basket of N assets is largely single-dimensional but their driving brownian motions are correlated. I suppose that we have already done c...
June 17th, 2021, 5:39 am
Forum: Off Topic
Topic: How to safeguard my research
Replies: 1246
Views: 141268

### Re: How to safeguard my research

I am writing this post to tell friends about my increasing persecution again. I mentioned that I used to buy 5 Liter Nestle water bottles but Nestle bottles that were manufactured in May 2021 were not good and I survived for a long time by buying 5L Nestle water bottles that had been lying in stores...
June 17th, 2021, 5:37 am
Forum: Technical Forum
Topic: Breakthrough in the theory of stochastic differential equations and their simulation
Replies: 1193
Views: 157165

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

I am writing this post to tell friends about my increasing persecution again. I mentioned that I used to buy 5 Liter Nestle water bottles but Nestle bottles that were manufactured in May 2021 were not good and I survived for a long time by buying 5L Nestle water bottles that had been lying in stores...
June 15th, 2021, 3:24 pm
Forum: Technical Forum
Topic: Breakthrough in the theory of stochastic differential equations and their simulation
Replies: 1193
Views: 157165

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

Explaining again, the above program makes a single step high order expansion of a single dimensional SDE and compares its density  with short stepping monte carlo simulation density of the same SDE.
June 15th, 2021, 3:03 pm
Forum: Technical Forum
Topic: Breakthrough in the theory of stochastic differential equations and their simulation
Replies: 1193
Views: 157165

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

I could not post the functions required for eighth order expansion since they increased the size of maximum characters in a single post. I am posting them here. . . function [IntegralCoeff] = ComputeIntegralCoeffsOrder8() IntegralCoeff(1:3,1:3,1:3,1:3,1:3,1:3,1:3,1:3)=0; %IntegralCoeffdt(1:3,1:3,1:3...
June 15th, 2021, 2:51 pm
Forum: Technical Forum
Topic: Breakthrough in the theory of stochastic differential equations and their simulation
Replies: 1193
Views: 157165

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

Friends here is the program for SDE series expansion order  4-12. I have given some instructions at the start how to change order of the program. . function [] = NewHermiteExpansionO8() %Copyright Ahsan Amin. Infiniti derivatives Technologies. %Please fell free to connect on linkedin: linkedin.com/i...
June 14th, 2021, 4:22 pm
Forum: Technical Forum
Topic: Breakthrough in the theory of stochastic differential equations and their simulation
Replies: 1193
Views: 157165

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

I completed work on 12th order Ito-Taylor expansion of a single SDE and I will soon(in another day) posting my all my high order expansion programs so friends can play with and compare 4th, 8th and 12th order expansions in both original and bessel coordinates.  I will also be (hopefully tomorrow or ...
June 13th, 2021, 6:32 pm
Forum: Technical Forum
Topic: Breakthrough in the theory of stochastic differential equations and their simulation
Replies: 1193
Views: 157165

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

Friends, I had been thinking about organization of my new program but then I wanted to ask the question whether we could take a large step for stochastic volatility SDE using higher order asymptotic expansion. If we cannot take a large step with SV SDE with accuracy, then there is no point in applyi...
June 9th, 2021, 8:44 am
Forum: Technical Forum
Topic: Breakthrough in the theory of stochastic differential equations and their simulation
Replies: 1193
Views: 157165

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

Friends, we have been  working for a long time with solution of SDEs and it seems reasonable that we need to at least achieve our benchmark of stochastic volatility option pricing with one SDE specified for asset price and another SDE specified for stochastic volatility and a description of correla...
June 7th, 2021, 1:35 pm
Forum: Technical Forum
Topic: Breakthrough in the theory of stochastic differential equations and their simulation
Replies: 1193
Views: 157165

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

Here is a sample Nasdaq ITCH file that I downloaded several years ago and I am attaching it for friends to be able to run it with my C++ program that I uploaded two posts ago.
20150109_EBAY.zip
June 7th, 2021, 1:25 pm
Forum: Technical Forum
Topic: Breakthrough in the theory of stochastic differential equations and their simulation
Replies: 1193
Views: 157165

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

Friends, we have been  working for a long time with solution of SDEs and it seems reasonable that we need to at least achieve our benchmark of stochastic volatility option pricing with one SDE specified for asset price and another SDE specified for stochastic volatility and a description of correlat...
June 7th, 2021, 1:07 pm
Forum: Technical Forum
Topic: Breakthrough in the theory of stochastic differential equations and their simulation
Replies: 1193
Views: 157165

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

Friends, I still could not add comments therefore I have given a brief overview of program logic and I am posting the programs. There are just two files in my program. A header file and a .cpp file.  My algorithm for limit order book construction is very different. There are two deques for "bid...