A multidimensional transform for pricing American options under stochastic volatility models

Natalia Beliaeva; Ye Chen; Sanjay Nawalkha

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This paper presents a multidimensional transform-based approach for pricing American options, which allows the construction of simple path-independent lattices for stochastic volatility models.
We demonstrate that using simple recombining trees can price American options under very general stochastic volatility models, and the transform-based approach is computationally efficient and accurate.
We prove the convergence of discrete-time processes to continuous-time processes under stochastic volatility models, such as Heston (1993), Hull and White (1987), and others.

Abstract

This paper presents a transform-based approach for pricing American options under stochastic volatility models. The multidimensional transform-based method allows for the construction of simple path-independent lattices for both one- and two-volatility- factor stochastic volatility models. We construct simple path-independent lattices and prove the convergence of the discrete processes to the underlying continuous ones. Our transform-based approach is computationally efficient and accurate for pricing American options under low-dimensional stochastic volatility models.

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