From: "Robert H. Berman"
Subject: Re: finite elements in math. finance
Date: Fri, 5 Mar 1999 09:20:13 -0500
Newsgroups: sci.math.num-analysis
PDEase2D, which solves PDEs numerically via finite elements, has over 15
sample problems involving options and finance using Black-Scholes equation.
These sample problems are available with the new Macsyma 2.4 and PDEase demo
from http://www.macsyma.com
Here is a partial list:
OPTIONPR Black-Scholes option pricing stochastic PDE
ASYMMETRIC POWER OPTION Black-Scholes option pricing with asymmetric
power
BASKET WITH CAP Black-Scholes model of capped basket
CAPPED ASYMMETRIC POWER OPTION Black-Scholes option pricing with
asymmetric power and cap
CALL ON BASKET Black-Scholes option pricing with basket
DOUBLE BARRIER Black-Scholes pricing of double knock-out options
DOUBLE BARRIER BASKET Black-Scholes pricing of Double knock-out options
with basket
PLAIN VANILLA EUROPEAN Black-Scholes model of simple European options
DOUBLE BARRIER Black-Scholes model of knock-out call options with two
barriers
SINGLE BARRIER Black-Scholes model of option pricing of single barrier
knock-out calls
SINGLE BARRIER BASKET Black-Scholes model of single barrier knock-out
call and basket
SINGLE BARRIER TIME DEPENDENT REBATE Black-Scholes model of option
pricing with time-dependent rebate
SINGLE BARRIER TIME DEPENDENT VOL Black-Scholes model of options with
time-dependent volatility
SINGLE REBATE BASKET Black-Scholes option pricing with basket and rebate
Many of these examples are contributed by Jurgen Topper, Arthur Anderson
Consulting, juergen.topper@de.arthurandersen.com He has writen about
financial models with finite elements and may have working papers available.
There is considerable literature about this topic.
Hope this helps.
Bob Berman
Robert H. Berman Tel: 781-646-4550
Macsyma Inc. Fax: 781-646-3161
20 Academy Street Email: berman@macsyma.com
Arlington, MA 02476-6436 USA URL: http://www.macsyma.com
Ben Crain wrote in message <36DF3C7A.C78A5E01@gmu.edu>...
>Would greatly appreciate info/references to the use/application of the
>finite element method to the solution
>of pde's arising in mathematical finance (esp. derivatives
>pricing/modeling). Anything on this topic would be useful: concrete
>examples, theoretical discussions, etc. I don't need references to
>finite elements per se (I'm up to my eyeballs in the math. theory of
>finite elements), but want to know if/how it can be/has been applied to
>pde's in math. finance.
>
>Thanks, Ben Crain
>bcrain@gmu.edu
>
==============================================================================
From: spellucci@mathematik.tu-darmstadt.de (Peter Spellucci)
Subject: Re: finite elements in math. finance
Date: 5 Mar 1999 15:36:24 GMT
Newsgroups: sci.math.num-analysis
In article <36DF3C7A.C78A5E01@gmu.edu>,
Ben Crain writes:
|> Would greatly appreciate info/references to the use/application of the
|> finite element method to the solution
|> of pde's arising in mathematical finance (esp. derivatives
|> pricing/modeling). Anything on this topic would be useful: concrete
|> examples, theoretical discussions, etc.
maybe the following helps:
'Mathematics of Financial Derivatives: a Student Introduction'. P.
Wilmott, J.N. Dewynne and S.D. Howison.) Cambridge University Press,
1995.
'Option Pricing: Mathematical Models and Computation'. P. Wilmott, J.N.
Dewynne and S.D. Howison. Oxford Financial Press, 1993.
peter