Pricing bivariate option under GARCH processes with time-varying copula

Abstract

This paper develops a method for pricing bivariate contingent claims under General Autoregressive Conditionally Heteroskedastic (GARCH) process. As the association between the underlying assets may vary over time, the dynamic copula with time-varying parameter offers a better alternative to any static model for dependence structure and even to the dynamic copula model determined by dynamic dependence measure. Therefore, the proposed method proves to play an important role in pricing bivariate options. The approach is illustrated with one type of better-of-two-markets claims: call option on the better performer of Shanghai and Shenzhen Stock Composite Indexes. Results show that the option prices obtained by the time-varying copula model differ substantially from the prices implied by the static copula model and even the dynamic copula model derived from the dynamic dependence measure. Moreover, the empirical work displays the advantages of the suggested method.