A Fast Method for the Computation of Option Prices Based on the N-Point Pade Approximant

This paper develops a fast method for the computation of option prices for models whose characteristic function is time-consuming to compute due to the need to solve ordinary differential equations or difference equations numerically, which is the case for a wide class of models of stocks, bonds, or currencies, including the general affine jump-diffusion models, quadratic-Gaussian models, and the GARCH option pricing models. This paper shows that approximating the model's cumulant generating function as a rational function of polynomials (Pade approximant form) within the saddlepoint approach of Lugannani and Rice leads to a fast and accurate computation of option prices. For most practical purposes, 2~3 evaluations of the cumulant generating function (characteristic function) turn out to be sufficient to get an accurate approximation of the cumulative distribution function that appears in the option price formula