Pricing American Option Based on a Chebyshev Approximation of the Early Exercise Boundary

In this paper we introduce a new method of pricing an American call option by approximating its early exercise boundary based on Chebyshev polynomial functions. We implement the method to price options under the standard assumptions of the Black-Scholes model, for European options, and under stochastic volatility. For the latter, we provide an integral representation which unbundles the American call option price to Arrow-Debreu security prices. Numerical results indicate that our method is an effective alternative to other exercise boundary approximation methods under both the standard assumptions of the Black-Scholes and stochastic volatility