American Option Pricing Under GARCH With Non-Normal Innovations

Abstract

As it is well known from the time-series literature, GARCH processes with non-normal shocks provide better descriptions of stock returns than GARCH processes with normal shocks. However, in the derivatives literature, American option pricing algorithms under GARCH are typically designed to deal with normal shocks. We thus develop here an approach capable of pricing American options with non-normal shocks. The approach uses an equilibrium pricing model with shocks characterized by a Johnson Su distribution and a simple algorithm inspired from the quadrature approaches recently proposed in the option pricing literature. Numerical experiments calibrated to stock index return data show that this method provides accurate option prices under GARCH for non-normal and normal cases.

Keywords: American Options, GARCH, Non-Normal Distribution, Quadrature

JEL Classification: C63, G13