Transform Analysis for Pricing American Options under Low-Dimensional Stochastic Volatility Models

This paper presents a new transform-based approach for path-independent lattice construction for pricing American options under low-dimensional stochastic volatility models. We derive multidimensional transforms which allow us to construct efficient path-independent lattices for virtually all low-dimensional stochastic volatility models given in the literature including one volatility factor-based stochastic volatility (SV) models, two volatility factors-based SV models, stochastic volatility jump (SVJ) models with one and two jump factors in the asset returns, and SVJ models with jumps in both asset returns and volatility. The lattice-based approximations of the prices of European options converge rapidly to their true prices obtained using quasi-analytical solutions