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Yani Boshev


Total Posts: 1
Joined: Jul 2013
 
Posted: 2013-07-02 18:52
I am trying to implement an algorithm in Matlab which solves the PIDE for pricing European options under the aforementioned model. I use Yanenko splitting scheme in order to receive the price of the option under stochastic volatility without jumps. For the jump process I think to use Fast Fourier Transform function in Matlab. Under the integral part of the equation (jump process) I made the required substitutions in order to receive convolution property of the integral. I assume that the jump size follows lognormal distribution so I took and log(price of the underlying). I also use probability density function of the normal distribution for generated values of the log(jump sizes) so I have a vector with probabilities of the relative jump size. So my idea is as follows.
1. I take the received value of the option under stochastic volatility, Fourier Transform.
2. Fourier Tranform of the vector with probabilities of the relative jump sizes.
3. Multiply both transformed functions (property of the convolution).
4. Inverse Fourier Transform.

After taking exponential of the received value this must be the value of the option.
Am I right? If you see any mistakes, please comment.

pj


Total Posts: 2862
Joined: Jun 2004
 
Posted: 2013-07-23 17:42
If the jumps are independent of the stochastic volatility,
it is correct.

Just be sure that your precision is not way too low.

вакансия "Программист Психологической службы" -але! у нас ошибко! не работает бля-бля-бля -вы хотите об этом поговорить?

Lapsilago


Total Posts: 5
Joined: Nov 2005
 
Posted: 2013-08-07 08:39

Hi,

you can find everything here:

http://www.nuclearphynance.com/Show%20Post.aspx?PostIDKey=163178

The code is available via Matlab fileexchange.

 

Best, Lapsi

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