Dynamic Programming Approach for Valuing Options in the GARCH Model

Dynamic Programming Approach for Valuing Options in the GARCH Model

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Article ID: iaor200942173
Country: United States
Volume: 55
Issue: 2
Start Page Number: 252
End Page Number: 266
Publication Date: Feb 2009
Journal: Management Science
Authors: , ,
Keywords: programming: dynamic
Abstract:

In this paper, we develop an efficient algorithm to value options under discrete–time GARCH processes. We propose a procedure based on dynamic programming coupled with piecewise polynomial approximation to compute the value of a given option, at all observation dates and levels of the state vector. The method can be used for the large GARCH family of models based on Gaussian innovations and may accommodate all low–dimensional European as well as American derivatives. Numerical implementations show that this method competes very advantageously with other available valuation methods.

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