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

Authors:
M. Esteban-Bravo;J. M. Vidal-Sanz
Affiliations:
-;-
Venue:
Computers & Mathematics with Applications
Year:
2006

Citing 7
Cited 0

A Theory for Multiresolution Signal Decomposition: The Wavelet Representation

IEEE Transactions on Pattern Analysis and Machine Intelligence
Adapted solution of a backward stochastic differential equation

Systems & Control Letters
Wavelets: a tutorial in theory and applications

Wavelets: a tutorial in theory and applications
Spherical algorithms and evaluation of the fixed point set

Nonlinear Analysis: Theory, Methods & Applications
Convergence estimates for the wavelet Galerkin method

SIAM Journal on Numerical Analysis
Weak approximations. A Malliavin calculus approach

Mathematics of Computation
Global optimization in Rn with box constraints and applications: A Maple code

Mathematical and Computer Modelling: An International Journal

Quantified Score

Hi-index	0.09

Visualization

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.