Numerical pricing of European options with arbitrary payoffs

Abstract

In this paper we introduce the CHEB method, a quadrature-based methodology for the fast and accurate pricing of European options with arbitrary payoffs. The method comes as a natural application of Chebfun, a numerical computing software package built on the approximation properties of Chebyshev series and Chebyshev interpolants. For the methodology to be useful for practical purposes, we address two considerations: the recovery of the underlying’s density from the characteristic function, and the estimation of the truncation error. The methodology can be viewed as an extension of the COS method, a quadrature-based methodology designed for the pricing of standard, non-arbitrary payoffs.