Valuation of American Option Prices Under the Double Exponential Jump Diffusion Model with a Markov Chain Approximation

Abstract

This paper suggests a numerical method for valuation of American options under the Kou model (double exponential jump diffusion model). The method is based on approximation of underlying asset price using a finite-state, time-homogeneous Markov chain. We examine the effectiveness of the proposed method with simulation results, which are compared with those from the conventional numerical method, the finite difference method for PIDE (partial integro-differential equation).

Valuation of European and American Option Prices Under the Levy Processes with a Markov Chain Approximation

“…More generally, Këllezi and Webber (2004) and Maller et al (2006) suggested a lattice method for an infinite activity Lévy case. And Han (2012) and Simonato (2011) proposed the option pricing method based on a Markov chain under a Lévy process very lately. Simonato (2011) applied the method only to the Merton's jump diffusion model because the transition density, the density of the logarithmic stock price change, derives easily in closed form Merton (1976).…”

“…Simonato (2011) applied the method only to the Merton's jump diffusion model because the transition density, the density of the logarithmic stock price change, derives easily in closed form Merton (1976). In Han (2012), since there is no closed form of the transition density in the Kou's double exponential jump diffusion model, the second order approximation of the transition density was calculated and used to value American option prices Kou (2002). So far, there is no study about numerical option pricing with direct use of the stock price distribution in the Lévy processes with infinite activity pure jumps.…”