A GARCH Option Pricing Model with Filtered Historical Simulation
提出一种基于GARCH模型和滤波历史创新的期权定价新方法，允许历史与定价收益分布不同，用标普500指数期权数据验证其优于其他GARCH和Black-Scholes模型，并解释了隐含波动率微笑现象。
We propose a new method for pricing options based on GARCH models with filtered historical innovations. In an incomplete market framework, we allow for different distributions of historical and pricing return dynamics enhancing the model flexibility to fit market option prices. An extensive empirical analysis based on S&P 500 index options shows that our model outperforms other competing GARCH pricing models and ad hoc Black-Scholes models. We show that the flexible change of measure, the asymmetric GARCH volatility and the nonparametric innovation distribution induce the accurate pricing performance of our model. Using a nonparametric approach, we obtain decreasing state price densities per unit probability as suggested by economic theory and corroborating our GARCH pricing model. Implied volatility smiles appear to be explained by asymmetric volatility and negative skewness of filtered historical innovations.