Pricing American Options Under Stochastic Volatility: A New Method Using Chebyshev Polynomials to Approximate the Early Exercise Boundary

U of London Queen Mary Economics Working Paper No. 488

46 Pages Posted: 17 May 2003

See all articles by Elias Tzavalis

Elias Tzavalis

University of London - Queen Mary - Department of Economics

Shijun Wang

Queen Mary, University of London - Department of Economics

Date Written: February 2003

Abstract

This paper presents a new numerical method for pricing American call options when the volatility of the price of the underlying stock is stochastic. By exploiting a log-linear relationship of the optimal exercise boundary with respect to volatility changes, we derive an integral representation of an American call price and the early exercise premium which holds under stochastic volatility. This representation is used to develop a numerical method for pricing the American options based on an approximation of the optimal exercise boundary by Chebyshev polynomials. Numerical results show that our numerical approach can quickly and accurately price American call options both under stochastic and/or constant volatility.

JEL Classification: G12, G13, C63

Suggested Citation

Tzavalis, Elias and Wang, Shijun, Pricing American Options Under Stochastic Volatility: A New Method Using Chebyshev Polynomials to Approximate the Early Exercise Boundary (February 2003). U of London Queen Mary Economics Working Paper No. 488. Available at SSRN: https://ssrn.com/abstract=381220 or http://dx.doi.org/10.2139/ssrn.381220

Elias Tzavalis (Contact Author)

University of London - Queen Mary - Department of Economics ( email )

Mile End Road
London, E1 4NS
United Kingdom

HOME PAGE: http//www.qmw.ac.uk/~ugte184/

Shijun Wang

Queen Mary, University of London - Department of Economics ( email )

Mile End Road
London, E1 4NS
United Kingdom

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