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Nov 15

Garch option pricing

Posted by abiao at 13:54 | Code » Matlab | Comments(4) | Reads(15123)
We all know one assumption of Black Scholes model is constant volatility during option period, which has been relaxed by several methods including Heston stochastic volatility, SABR stochastic volatility, etc. Here is another way proposed by Jin-Chuan Duan, Geneviève Gauthier, and Jean-Guy Simonato in their paper "An analytical approximation for the GARCH option pricing model" published at the Journal of computational finance in 1999, http://www.journalofcomputationalfinance.com/public/showPage.html?page=1112.
GARCH option pricing framework has been developed in recent years. However, an efficient method for computing option prices in this framework remains lacking. In this article, a fast analytical approximation is developed for computing European option prices in the GARCH framework. The approach, following that of Jarrow and Rudd (1982), uses the Edgeworth expansion of the risk-neutral density function. Analytical expressions for the first four moments of the cumulative asset return over any horizon under the GARCH model are derived in this paper. A numerical analysis shows that these moment formulas are accurate under fairly general conditions. The analytical GARCH option pricing formula based on the Edgeworth expansion is found to work well for short-maturity options. For long-maturity options, the approximate formula is generally satisfactory, except when the volatility dynamic of the GARCH model exhibits an extremely high level of persistence.

Matlab codes can be downloaded at http://www.rmi.nus.edu.sg/DuanJC/l, several other programming files can be also found at the page, for example, Co-integration option pricing model, GARCH option pricing model and its application to volatility smile, Linear and non-linear asymmetric GARCH models, Estimating exponential affine term structure models, and Maximum likelihood estimation method for Merton's deposit insurance pricing model.

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The link for the code is not working. I thing itcould be helpfull for me, is it possible to fix it? thanqs
thanks for pointing the issue out, I have updated the link, cheers.
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