Pricing bivariate option under GARCH-GH model with dynamic copula: application for Chinese market

Abstract

This paper develops the method for pricing bivariate contingent claims under general autoregressive conditionally heteroskedastic (GARCH) process. In order to provide a general framework being able to accommodate skewness, leptokurtosis, fat tails as well as the time-varying volatility that are often found in financial data, generalized hyperbolic (GH) distribution is used for innovations. As the association between the underlying assets may vary over time, the dynamic copula approach is considered. Therefore, the proposed method proves to play an important role in pricing bivariate option. The approach is illustrated for Chinese market with one type of better-of-two markets claims: call option on the better performer of Shanghai Stock Composite Index and Shenzhen Stock Composite Index. Results show that the option prices obtained by the GARCH-GH model with time-varying copula differ substantially from the prices implied by the GARCH-Gaussian dynamic copula model. Moreover, the empirical work displays the advantage of the suggested method.

Keywords:

• call-on-max option
• GARCH process
• generalized hyperbolic (GH) distribution
• normal inverse Gaussian (NIG) distribution
• copula
• dynamic copula

JEL Classification Codes :

• C51
• G12

Acknowledgements

The authors wish to thank the two referees for their precious remarks which permit to perform this paper.