A Fast Method for the Computation of Option Prices Based on the N-Point Pade Approximant
36 Pages Posted: 6 Jun 2011 Last revised: 12 Dec 2011
Date Written: June 5, 2011
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.
Keywords: options, saddlepoint method, N-point Pade approximants, rational function approximation
JEL Classification: C18, C63, G12, G13
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