Topics in Continuous-Time Finance; Spring 2003

Abstract

Answers must be handed in no later than at the lectures on Wednesday, April 9, 2003. Groups of 3 are OK; groups of 4 or more are not. Consider the parabolic PDE F t (x, t) + µ(x, t)F x (x, t) + 1 2 σ 2 (x, t)F xx (x, t) − r(x, t)F (x, t) :=(AF)(x,t) = h(x, t) (1) with terminal condition F (x, T) = g(x). We want to solve such problems (sometimes referred to as Cauchy problems) numerically by finite difference methods. As in Seydel Chapter 4, suppose the space/time domain has been discretized, and let w j i denote the finite difference approximation to F (x i , t j). For some θ ∈ [0; 1] we can construct a finite difference scheme by using