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

53 Pages Posted: 28 Dec 2009

See all articles by Natalia Beliaeva

Natalia Beliaeva

Suffolk University - Department of Finance

Sanjay K. Nawalkha

University of Massachusetts Amherst - Isenberg School of Management

Date Written: December 27, 2009

Abstract

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.

Keywords: American options, numerical methods, trees, Stocahstic volatility, jumps, SVJ

JEL Classification: G10, G11, G12, G13, G20, G21, G22, G23, G24

Suggested Citation

Beliaeva, Natalia and Nawalkha, Sanjay K., Transform Analysis for Pricing American Options Under Low-Dimensional Stochastic Volatility Models (December 27, 2009). Available at SSRN: https://ssrn.com/abstract=1528827 or http://dx.doi.org/10.2139/ssrn.1528827

Natalia Beliaeva

Suffolk University - Department of Finance ( email )

8 Ashburton Place-Beacon Hill
Boston, MA 02108-2770
United States

Sanjay K. Nawalkha (Contact Author)

University of Massachusetts Amherst - Isenberg School of Management ( email )

Amherst, MA 01003-4910
United States
413-687-2561 (Phone)

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