Modeling The Implied Volatility: An Empirical Study For HSI Options

Form various empirical work, it is well known that the implied volatilities differ for options that only differ in time to maturity and strikes, there are significant term structure and smile effects. We construct three models to try to explain the reasons form some different angels.First, the analysis of term structure of implied volatility, it is well known that the volatility of asset returns changes over time. This might be one of the reasons that implied volatilities differ for options that only differ in time to maturity. We construct models for the relation between short-and long-term implied volatilities based on some different assumptions of stock return volatility behavior, ie, AR,GARCH,E-GARCH,TARCH models. Second, the OLS model of the implied volatility, we adapt the parametric models to estimate the surfaces across moneyness and maturity. Third, we present a new model to recover the volatility of underlying asset form observed market option pricing with Dupire equation. Finally, We test these relations on HSI option data.Innovations:First, we test these relations with HIS data which are closed with china's security market. Second, we take long-term implied volatilities as the benchmark volatility in the term structure model and provide arbitrage strategies Third,we provide the economics explanations for Dupire equation.