Research On Pricing Of SSE 50ETF Option Based On GARCH Model

Option as a financial derivative products is a powerful tool for investors to hedge and hedging,due to the lack of risk aversion tools in China’s stock market,investors suffered heavy losses in the market.In order to cope with the demand for risk management,the Shanghai stock exchange launched the first exchange traded options-Shanghai 50ETF option in February 9,2015,investors in trading options,the first concern is whether the option is reasonable pricing.In 1973,Black and Scholes published "the pricing of options and corporate liabilities" papers,this paper calculated the theoretical price of any known term financial tools,put forward the B-S option pricing model,become a classic model in options pricing.The classical B-S model assumes that the volatility is constant.But the empirical research shows that the stock price volatility has the following characteristics:(1)the volatility smile.According to the assumptions of the B-S model,the implied volatility and the price is irrelevant and should be performed as a constant,but in fact at the money option implied volatility is less than the real value of the option and the virtual value option,so the implied volatility curve showing two upturned forms.(2)fat tailed distribution.In the extreme cases,the probability of asset return distribution is larger than the corresponding normal distribution,that is,the fat tail distribution.(3)the volatility clustering phenomenon,that is,large fluctuations followed by large fluctuations,small fluctuations followed by small fluctuations.This shows that the volatility is not a constant,but rather a time variant.After the empirical test,the GARCH model can solve the phenomenon of volatility clustering and peak thickness.The research object of this paper is the 16 year subscription option,which is listed in May 26th,and expires in July 27th,July.In the period of validity of the option,the average price of the option is 2.156 yuan.In order to analyze the effect of the model on the pricing of options,this paper select the implementation of the price of 1.95,2.15 and 2.25 of the options for pricing comparative analysis.Based on previous studies on the volatility of financial assets,this paper selects the GARCH model to estimate the volatility of the 50ETF option.Sample data is selected by the Shanghai 50ETF daily closing price since the Shanghai 50ETF options listed in February 9,2015 to May 25,2016.Because the rate of return on the assumption that the asset price is a continuous change,and the options B-S pricing model assumptions consistent,so first,to calculate the log yield of the SSE 50ETF with the daily closing price data.Then descriptive statistical analysis of the yield data,the results show that the yield is indeed a "peak fat tail" distribution,and there are fluctuations in the rate of aggregation phenomenon.This shows that the GARCH model is reasonable for the analysis of volatility in this paper.In the sample data through the stability test,and determine the optimal lag order through the AIC and SC criteria,the estimated mean equation and variance equation with yield data.This paper estimates the variance equation is used in GARCH,TGARCH and EGARCH model,the estimation results show that significant leverage coefficient TGARCH and EGARCH model are described,the Shanghai 50ETF has obvious "leverage effect",so the GARCH model is not suitable for the estimation of the volatility of Shanghai 50ETF.Next with the TGARCH and EGARCH models to predict the volatility of May 26th to July 27th.Then the predictions of the volatility and historical volatility into the B-S formula of real and imaginary value,fair value option pricing.Finally,it compares and analyzes the pricing results and the actual price of the options and explains the results.The results showed that:1)the pricing results of GARCH model are better than the historical volatility;this is because the GARCH model can capture the change of the underlying asset returns quickly compared with the historical volatility.2)the fair value of the option and the virtual value option pricing,TGARCH model,GARCH model in pricing results better than the EGARCH model,the TGARCH model can better fit and forecast the volatility of Shanghai 50ETF;3)in the three option,real option pricing of the highest accuracy,the virtual value option pricing method is the lowest.This is due to the small effect of real option price changes by the underlying asset volatility rate;by investor speculation,false value implied volatility overvalued option.This article is divided into six chapters.The specific chapters are as follows:The first part is the introduction,which is divided into four parts:the research background,purpose and significance,research methods,innovation and deficiencies,and structural framework.The second part is the literature review,respectively,the two aspects of the foreign scholars on the option pricing and volatility modeling are summarized.The third part is the introduction of the Black-Scholes option pricing model and the GARCH model.This part mainly summarizes the Black-Scholes option pricing model and the GARCH,EGARCH and TGARCH model in the GARCH model.The fourth part is based on the GARCH model family of volatility modeling and analysis,first of all the sample data to test,and then establish the mean equation and variance equation,and finally to establish the GARCH model for comparison and analysis.The fifthh part is the analysis of SSE 50ETF option pricing,the volatility and historical volatility forecasting GARCH model to rate into the B-S formula of real option pricing,fair value and virtual value,and analyze the pricing results.The last part is the conclusion,which summarizes the research of this paper.