Modeling The Implied Volatility Surface Based On Shanghai 50 ETF Options

Because Black-Scholes option-pricing model and traditional volatility model need stronger assumptions, which limited the scope of application of the models, so Scholars created volatility models based on market information-implied volatility surface model. The setting of implied volatility surface model is more flexible, it can capture more market information. Thus comparing with traditional volatility model (such as local volatility model), implied volatility surface model can better reflex the characteristics of the change of market, but the key to use is to set up matched implied volatility model according to the specific condition of market. Generally speaking, different market conditions need to set up different forms of models. Just in time our country launched Shanghai 50ETF option, hence we put it as the research object, trying to build a set of implied volatility surface model which is suitable for the characteristics of the Chinese market, wishing to provide some help to the pricing of index option and the corresponding risk management.First, this paper reviewed relative literature to know the research of the former scholar, discussed three mainstream deterministic implied volatility models in detail, cleared about the general characteristics and change rules of implied volatility surface model. Thus this paper set up five random implied volatility models those explained variable are the value degree and the residual time limit polynomial to study the cross section data of Shanghai 50ETF implied option volatility. The parameter estimation by these five models are unstable, have different degree of volatility over time, which conforms to the theoretical expectation.This paper chose the optimal model of the cross section according to the standard of sample fitting effect and out-samples predictive ability. The estimated parameter time series showed the phenomenon of autoregressive and correlation. So we set up VAR model based on parameter factor time series and use random walk model as the standard. Although VAR model can effectively reflect the characteristics of dynamic changes of implied volatility surface, but its estimation method is a two-step estimation method, which exist bigger risk of estimated error and not reliable result in theory.Then this paper established the equation system composed of three equations to describe the main characteristics of the dynamic change of implied volatility, these three equations respectively reflected the relationship between implied volatility, the value degree and residual maturity, autoregressive characteristics of parameter factors, parameter factors.Finally this paper tested robustness of these two models, increased the sample fitting data to confirm the conclusion of consistency in the cross section model, also excluded the influence of the special sample period by dividing subsample.Based on the analysis of the full text, we found the state-space model under the Kalman filtering method is better than VAR model and random walk model under two-stage estimation method. So the implied volatility equations set up by this paper under the Kalman filtering method can well depict the characteristics of dynamic change of Shanghai 50ETF option implied volatility surface. But this paper does not provide direct evidence that Kalman filtering method is better than two-step estimation method, the merits of two-step estimation method needs further research.