Pricing Bivariate Option Under Copula-GARCH Model

In this thesis,we study bivariate option pricing.The traditional Black-Scholes option pricing model is built on the assumption of normal distribution.However,a large number of empirical studies show that the normal distribution cannot well describe the rate of return on financial assets.In order to accurately price bivariate option,we apply normal inverse Gauss distribution(NIG)and GARCH model to capture the characteristics of skewness,fat tails,leptokurtosis and volatility clustering of rate of return,and link the marginal distribution of rate of return on assets with a copula function.In the end,copulaGARCH-Gauss model and copula-GARCH-NIG model are established.We also demonstrate how to calculate bivariate option prices under these models.In the empirical analysis,a two-step MLE procedure is used to estimate the parameters of multivariate Black-Scholes model,copula-GARCH-Gauss model and copula-GARCH-NIG model based on data of Dow Jones Industrial Average and NASDAQ index.And martingale pricing method is applied to price the European callon-max option under the above three option pricing models.The results show that the option price is more accurate under copula-GARCH-NIG model.The effect of Goorbergh's dynamic copula method will also be considered.