基于GARCH-GH模型的上证50ETF期权定价研究

Pricing SSE 50ETF Option under GARCH Model with Generalized Hyperbolic Innovations

上证50ETF期权是中国推出的首支股票期权.为描述上证50ETF收益率偏态、尖峰、时变波动率等特征,结合GARCH模型和广义双曲(Generalized Hyperbolic,GH)分布两方面的优势,建立GARCH-GH模型为上证50ETF期权定价.在等价鞅测度下,利用蒙特卡罗方法估计上证50ETF欧式认购期权价格.实证表明,相比较Black-Scholes模型和GARCH-Gaussian模型,GARCH-GH模型得到的结果更接近于上证50ETF期权的实际价格,其定价误差最小.

The SSE 50 ETF option is the first stock option in China.In order to capture skewness,leptokurtosis as well as the time varying volatility that are found in our dataset,this paper develops the GARCH-GH model that combines the two good features of GARCH models and of the generalized hyperbolic（GH） distribution for pricing the SSE 50 ETF option.Under the equivalent martingale measure,we obtain the estimated European call option price by using Monte Carlo method.Empirical results display the advantage of our method.Compared with the Black-Scholes model and the GARCH-Gaussian model,the option prices obtained by the GARCH-GH model are more close to the market price,and our model has minimal pricing error.