A Numerical Method for Pricing American-style Asian Options under Garch Model

This article develops a numerical method to price American-style Asian option in the context of the generalized autoregressive conditional heteroscedasticity (GARCH) asset return process. The development is based on dynamic programming coupled with the replacement of the normally distributed variable with a binomial one and the whole procedure is under the locally risk-neutral valuation relationship (LRNVR). We investigate the computational and implementation issues of this method and compare them with those of a candidate procedure which involves piecewise-polynomial approximation of the value function. Complexity analysis and computational results suggest that our method is superior to the candidate one and the generated GARCH option prices are capable of reflecting the changes in the conditional volatility of underlying asset.