Valuation of boundary-linked assets by stochastic boundary value problems solved with a wavelet-collocation algorithm

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Abstract

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.

Keywords

Stochastic boundary value problems
Financial derivatives
Wavelets
Collocation methods

Cited by (0)

We thank Professor A. Balbas and Professor E. Galperin for their helpful comments and suggestions. This research has been supported by two Marie Curie Fellowships of the European Community programme IHP under contract numbers HPMF-CT-2000-00781 and HPMF-CT-2000-00449, respectively.