Partial integro differential equation for levy processes

[tuko]

Hi everyone,

I´m trying to price european (and american) call option with partial integro differential equation,(stock price following levy process in general). But i´m having hard times to implement the code in matlab.

Could you please hepl in proving an example of code.

Thanks very much

 

[Nguyen]

Dear tuko

it seems you are doing very interesting problem. Would you mind posting a brief of your problem formulation so that we can have a brief idea what you are trying to do. In fact, by just looking at your one-page pdf file, I cannot know what you are trying to do and where you get stuck

 

[tuko]

Thanks for your answer .
I´m trying to approximate the equation using finite diference method, but i got stuck with the integral term, i cant figure out how to deal with in.

 

[Nguyen]

I also guess so ! The difficulties lie in Levy measure, but you could choose a Levy measure for your problem then it might be easier.
To deal with infinity upper/lower limits, I guess only way to do it is to map it into [0,1] interval

 

[Daniel Duffy]

I also guess so ! The difficulties lie in Levy measure, but you could choose a Levy measure for your problem then it might be easier.
To deal with infinity upper/lower limits, I guess only way to do it is to map it into [0,1] interval

The book by Cont and Tankov.

Here is also a pointer

http://www.datasimfinancial.com/UserFiles/articles/PIDE.pdf

Big, callenging poblem How good is your PDE/FDM?

 

[tuko]

That ´s exactly where I got stuck I chose Meixner process and it´s measure (I had to) but I ´m not able to move on with it.

 

[Nguyen]

Hey Daniel, interesting paper

 

[Nguyen]

tuko : if you can choose a Levy measure, I just guess (I might be wrong) that you could transform the lower/upper limit to [0,1] interval. Then apply the finite difference method for the integral equation. I am sure that you can google to find such methods

 

[tuko]

Daniel, thanks for your paper it´s really interesting.
I´ve tried to use the trapezoidal rule for the integral term (but only without transformation to [0,1], thanks Nguyen for your idea.)
But I think that my problem is the implementation in matlab.
Thanks for your help guys!!

 

[Daniel Duffy]

A really good project imo is to apply ADE to PIDE. Here is a paper (btw it uses transformation to [0,1])

This is starting to be used in practice and you could get an Msc/PhD from it, for sure (imho).

http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1552926

BTW search for QN article on Boost + PDE (using ADE)

 

[tuko]

Thanks so much Daniel, it seems like you are excellent in this problem