On the use of boundary conditions for variational formulations arising in financial mathematics

Abstract

The general intractability of derivative security valuation models to present techniques, both analytic and numerical, arguably remains one of the preeminant problem of mathematical finance. It is the focus of this paper to examine the applicability of a promising recent development, namely Radial Basis Functions (RBF), to the problem of option valuation. A Black–Scholes framework is considered for American and European options written on a one and two risky assets. The performance of RBF and Finite-Differencing algorithms are examined with respect to artificial boundary conditions, computational domain, domain decomposition, and mesh scaling.