help with pde
- To: mathgroup at smc.vnet.net
- Subject: [mg16110] help with pde
- From: "Will Holt" <will at aventura.freeserve.co.uk>
- Date: Thu, 25 Feb 1999 08:25:03 -0500
- Organization: Customer of Planet Online
- Sender: owner-wri-mathgroup at wolfram.com
Hi everyone, I am trying to solve the Black-Scholes pde in mathematica subject to the usual boundary conditions. 0.5*sigma^2*S^2*D[V[S,t],S,S]+r*S*D[V[S,t],S]-r*V[S,t]+*D[V[S,t],t] =0 V[0,T]=0,V[S,T]=Max[S-K,0], for some particular S, K and T. The Mathematica command "NDSolve" requires that the first argument must have both an equation and an initial condition. The problem is that the law motion for S is dS=alpha*S*dt+sigmadZ where dZ is a Wiener process that can be substituted by epsilon*SQRt[dt], with epsilon a random drawing from a standardised normal distribution. I thought that I did not have to include this law motion for S in NDSolve, but in case I do have to include it, how can I do this? Also, on a different issue, how can I generate three series of normal random numbers that are correlated amongst each other: rho12, rho23, rho13? e.g. dX1=rho12dX2+SQRT[1-rho12^2]*de12, with de12 a standard Wiener process independent of dX2, and so on for dX2 and dX3. Any help will be greatly appreciated. Will.