School of Economics and Finance

No. 488: Pricing American Options under Stochastic Volatility: A New Method Using Chebyshev Polynomials to Approximate the Early Exercise Boundary

Elias Tzavalis , Queen Mary, University of London
Shijun Wang , Queen Mary, University of London

February 1, 2003

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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.

J.E.L classification codes: G12, G13, C63

Keywords:American call option, Stochastic volatility, Early exercise boundary, Chebyshev polynomials