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