Risk Measure Of The Stock Index Options

This dissertation focused on the pricing models of stock index option and the parameters estimation of the stochastic process which its underlying assets obeys to, combining with CEV index option pricing models and the mainstream approach for the market risk management-VaR, we study on the market risk of stock index option.First, introduce VaR method which could identify the convexity or gamma risk. That is using second-order Taylor expansion approximation to describe the changes of option's value. According to Ito's Lemma, we derive the stochastic process by which option's value change follows in the relatively short holding period. Through the theory of VaR, European call stock index options VaR's formula, based on the underlying asset, is derived from DGT approximation method; Referring to the option VaR computation principle under B-S model, we conclude analysis formula of that under CEV model.Next, through the implicit parameter estimate law, using S&P CNX the Nifty stock index option's history data, we had estimated the CEV option pricing model's parameter, combined it with the above two kinds of stock index option risk's formula, the S&P CNX Nifty stock index option's risk can be measured. In view of the success rate, both of which have passed the test; But considering the availability of stock index options data, the analysis formula have an advantage over that of DGT, whose mean square error were larger than the former. In addition, for S & P CNX Nifty index options data, historical simulation method, Monte Carlo simulation, GARCH Model are used to measure their risks separately, and compared them with that of VaR calculation formula above. The results show that the VaR calculation formula based on the CEV model is better.Third, by taking second-order Taylor approximation, we had simplified GMM moment conditions of the CEV process, combined with historical data on the Shanghai and Shenzhen 300 stock index to estimate the parameters of the CEV model. Using GARCH model to fit the Shanghai and Shenzhen 300 stock index return data, we obtained the volatility in the Shanghai and Shenzhen 300 stock index return, associate with the definition of constant elasticity of variance, calculates the priori distribution of the CEV process parameters', then the MCMC method could be used in the CEV parameter estimation. And the estimation error is relatively small, that the parameter estimation is more accurate than that of GMM. With the result of the parameters, the Shanghai and Shenzhen 300 stock index options'VaR can be measured by the DGT approximation and the analysis formula separately. The result shows that without real index option's data, the former is more accurate than the latter. And according to the Indian S & P CNX Nifty index of Venture empirical conclusion that these two different perspectives of risk calculation formula can be applied to China's launch of stock index Option Risk Measurement.