A Spectral Element Approximation to Price European Options. II. The Black-Scholes Model with Two Underlying Assets

Authors:
Wuming Zhu;David A. Kopriva
Affiliations:
Department of Mathematics, Florida State University, Tallahassee, USA;Department of Mathematics, Florida State University, Tallahassee, USA
Venue:
Journal of Scientific Computing
Year:
2009

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Abstract

We develop a Legendre quadrilateral spectral element approximation for the Black-Scholes equation to price European options with two underlying assets. A weak formulation of the equations imposes the boundary conditions naturally along the boundaries where the equation becomes singular. As examples, we apply the method to price European rainbow and basket options. We compare the efficiency for fully implicit and IMEX integration of the equations in time, three iterative solvers and two diagonal preconditioners. Of the choices, we find that GMRES with a fully implicit approximation in time, preconditioned with the mass matrix is the most efficient.