Gaussian Quadrature Method for Pricing American and Exotic Options in a Jump-Diffusion Process

In this paper we propose a Gaussian quadrature method to study American and exotic option pricing under the jump-diffusion model of Merton (1976). Our numerical experiments show that the Gaussian quadrature method, compared to several existing methods in the literature, including the fast Gauss transform method (Broadie and Yamamoto, 2003), the bivariate tree approach (Hilliard and Schwartz, 2005), and the extrapolation approach (Feng and Linetsky, 2008), is accurate for valuing American options. In addition to American options, we also show that the Gaussian quadrature method performs well for the valuation of exotic options under the jump-diffusion model. Overall, the Gaussian quadrature method is highly accurate and suitable for the valuation of price options with early exercise features under a jump-diffusion process