Option-implied Density,Extreme Value Distribution And Tail Risk-

According to Bliss and Panigirtzoglou(2002),as well as Figlewski(2009),we estimate 50ETF Option-Implied Density and test its information contents.Based on the formula given by Breeden and Litzenberger(1978),we use cubic spline to fit the"Volatility Smile" of 50ETF Options,and then obtain the Option-Implied Density.Since the range of strikes available from the market is finity,the Gerneralized Extreme Value Distribution(GEV Distribution)is employed to complete the Option-Implied Density,so that it is appropriate for modelling the "fat tail" of financial asset return.We first simulate option prices and find our GEV-based method is accurate and stable.Also,we employ two alternative methods.One is the method based on Black-Scholes(BS)Pricing Formula,the other is the method based on the "horizontal extrapolation".Simulation results show that the GEV-based method is superior.Based on China's 50 ETF option data,we estimate 50ETF Option-Implied Density and its implied moments.Empirically,we find that the implied moments possess the information content in forecasting the future realized moments.Also,they make contribution in forecasting market crash risk.The "shape parameter",or "implied tail",which belongs to the GEV Distribution,can be served as the market expectation about the probability of future boom and crash.We find that the "implied tail" has the information in forecasting future boom and crash,but the forecasting ability is weak.Finally,in order to better demonstrate the effectiveness of using the GEV Distribution to model the "fat tail" of financial asset return,we employ the framework proposed by Alentorn and Markose(2008)and calculate the "Value at Risk"(VaR)from the GEV-based Option-Implied Density.VaR metric is also calculated from BS-based and "horizontal extrapolation"-based Option-Impled Density.Backtesting results show that the GEV-based method is superior.