The Construction And Parameter Calibration Of The Implied Volatility Surface Of SSE 50ETF Options

Implied volatility is a core factor affecting option pricing.In actual transactions,the implied volatility of different moneyness k and different maturity are all different.The implied volatility surface is a three-dimensional surface constructed with the moneyness k as the x-axis,the maturity ? as the y-axis and the implied volatility corresponding to(k,?)as the z-axis.The implied volatility of different moneyness in the same maturity forms a “volatility smile” curve,and the implied volatility model is a model depicting this curve.For the Chinese options market,predecessors have conducted empirical analysis on Heston model,Stochastic Alpha,Beta,Rho(SABR)model etc.This thesis introduces two other types of implied volatility models,stochastic volatility inspired(SVI)model and Wing Model.The main work and innovations include:1.This thesis introduced the SVI and Wing Model implied volatility model into the Chinese options market.The Quasi-Explicit method(sequential least squares programming algorithm and Nelder-Mead simplex algorithm)are used to estimate the five parameters of the SVI model in two steps.The parameters of the Wing Model are divided by type and then estimated by the nonlinear least square method and their parameters are calibrated using high-frequency data for 1 minute.Finally,by using two-dimensional cubic spline interpolation method to interpolate the implied volatility of k and ? directions respectively,the three-dimensional implied volatility surface of SVI model and Wing Model is obtained.2.Shanghai stock exchange 50 ETF options data is used to do empirical analysis of SVI model and Wing Model.The procedure of Wing Model parameter estimation is designed and the parameter calibration method is proposed combining a large number of statistical tests.The three-dimensional surfaces of the SVI model and Wing Model volatility for the Shanghai stock exchange 50 ETF options are given.Compared with the SABR model,we find that the SVI and Wing Model volatility model's fitting effect on the market volatility is very accurate,and the total sum of square error reaches below 10-3.Both are far better than the SABR model.In addition,both the SVI and Wing Model volatility models overcome the problem that the SABR model cannot accurately fit the implied volatility of all maturity options.This thesis demonstrates with examples that the SVI and Wing Model volatility models can be used as a powerful tool for China's options investors to manage volatility and options portfolios,and also have a certain construction significance for the reasonable pricing and steady development of China's financial derivatives market.