A Simple Approach to Pricing American Options Under the Heston Stochastic Volatility Model

Abstract

In a recent paper, NBZ [2010] present a multidimensional transform for generating path-independent trees for pricing American options under low dimensional stochastic volatility models. For this class of models, this approach has higher accuracy than the GARCH tree method of Ritchken and Trevor [1999], and is computationally more efficient than the Monte Carlo regression method of Longstaff and Schwartz [2001] as well as the lattice method of Leisen [2000]. In this paper, we give an explicit demonstration of the NBZ transform using the specific example of the Heston [1993] stochastic volatility model. This approach obtains highly accurate American option prices within a fraction of a second using the control variate method.

Keywords: Heston, options, stochastic volatility, American options, trees

JEL Classification: G0, G11, G12, G13, G20, G21, G22, G23, G24