Valuation of boundary-linked assets by stochastic boundary value problems solved with a wavelet-collocation algorithm
This article studies the valuation of boundary-linked assets and their derivatives in continuous-time markets. Valuing boundary-linked assets requires the solution of a stochastic differential equation with boundary conditions, which, often, is not Markovian. We propose a wavelet-collocation algorithm for solving a Milstein approximation to the stochastic boundary problem. Its convergence properties are studied. Furthermore, we value boundary-linked derivatives using Malliavin calculus and Monte Carlo methods. We apply these ideas to value European call options of boundary-linked assets. (c) 2006 Elsevier Ltd. All rights reserved.
stochastic boundary value problems financial derivatives wavelets collocation methods