A NUMERICAL METHOD FOR PRICING AMERICAN-STYLE ASIAN OPTIONS UNDER GARCH MODEL

Dan Shao ()
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Dan Shao: Department of Economics, Faculty of Arts and Social Sciences, National University of Singapore, AS2 Level 6, 1 Arts Link, Singapore 117570, Singapore

International Journal of Theoretical and Applied Finance (IJTAF), 2006, vol. 09, issue 08, 1323-1350

Abstract: 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.

Keywords: GARCH process; heteroscedasticity; Asian options; American options; dynamic programming; piecewise polynomial (search for similar items in EconPapers)
Date: 2006
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DOI: 10.1142/S0219024906003986

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