An Analytical Approximation for Option Price under the Affine GARCH Model - A Comparison with the Closed-Form Solution of Heston-Nandi

Abstract

In the option pricing theory, two important approaches have been developed to evaluate the prices of a European option. The first approach develops an almost closed-form option pricing formula under a specific GARCH process (Heston & Nandi, 2000). The second approach develops an analytical approximation for computing European option prices with more widespread NGARCH models (Duan, Gauthier & Simonato, 1999). The analytical approximation was also developed under GJR-GARCH and EGARCH models by Duan, Gauthier, Sasseville & Simonato (2006). However, no empirical work was performed to study the comparative performance of these two formulas (closed-form solution and analytical approximation). Also, it is possible to develop an analytical approximation under the specific GARCH model of Heston & Nandi (2000). In this paper, we have filled up those gaps. We started with the development of an analytical approximation, for computing European option prices, under Heston-Nandis GARCH model. In the second step, we carried out a comparative analysis of the three formulas using CAC 40 index returns from 31 December 1987 to 31 December 2013.

Keywords: GARCH, Option, Pricing, Approximation, Performance, Hedging

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