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Finite element method in finance

featips

Joined
2/26/09
Messages
76
Points
16
Hi,

I am a PhD student in computational mechanics, focusing on finite element methods (FEM), also a dual degree 1st year student in MFE.

I ever used both finite difference method (FDM) and FEM, and know much about the comparisons between these two numerical methods. However, all these knowledge are just in engineering field. Now, since I am still a 1st year MFE student, I still have not get a 'big' picture of financial engineering modeling. Therefore, I still can not figure out the the comparison between FEM and FDM in finance. In my 'computational finance' courses only finite didifference (FDM) and Monte Carlo methods are touched, no FEM. The professor of that course looks like do not have too much background and interest in FEM........ There are one or two books talkes about FEM in FE (I havn't got a chance to read them, but will do...)

So, my questions are:

(1) How is the application of FEM in finance? How many people in finance have interest and are using FEM? In engineering there are lots of problems that can not be solved by FDM, but can be easily solved with FEM. Are there similar cases in finance?

(2) Even though now FEM may not be widely used in finance, do you guys think in future FEM will gain more applications? I plan to find a quant job, and definitely hope to take advantage of my phd background in FEM, so this is important for me.

Your input is greatly appreciated.
 
Here are my impressions/experience

1) How is the application of FEM in finance? How many people in finance have interest and are using FEM? In engineering there are lots of problems that can not be solved by FDM, but can be easily solved with FEM. Are there similar cases in finance?

FEM is not used so much when compared to FDM and MC.
Finance applications are not the same as engineering and FEM is overkill. Of course, it can be done but is a sledgehammer.
FEM has no critical mass in computational finance, it would seem.

(2) Even though now FEM may not be widely used in finance, do you guys think in future FEM will gain more applications? I plan to find a quant job, and definitely hope to take advantage of my phd background in FEM, so this is important for me.

Personally, I don't think so. I would learn FEM and FDM. FDM is used a lot and having it on your resume/CV would be good imho.

Here is a link to the Heston model (pdf) solved by FDM. Kluge has a FEM solution.
Datasim Financial Forums | View topic - Robust FDM for Heston and SABR models (Roelof Sheppard)

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For the record, I (Duffy) did 2 research degrees in FEM and FDM and have used them in industry. I have written a book on FDM for derivatives pricing.
 
Hi featips,

first I've to recommend Duffy's books!
Nevertheless some problems open up by using FDM/FEM in high-dimensional problems. So in financial engineering MC methods work well.
 
The FEM book for derivatives by Juergen Topper is worth getting. He models options in 1,2 and 3 factors.
The material can be read without any prior knowledge of FEM.
 
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