International Journal of Financial Management

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


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1 BESTMOD, Higher Institute of Management, Tunis, Tunisia
     

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

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Authors

Noureddine Lahouel
BESTMOD, Higher Institute of Management, Tunis, Tunisia
Slaheddine Hellara
BESTMOD, Higher Institute of Management, Tunis, Tunisia

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-Nandi's 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.

References