Modeling And Applications Of Option Implied Volatility Surface

Options contain a lot of information.Many scholars at home and abroad have proposed various methods to extract rich implicit information from options in both mature and emerging markets.Most of relevant popular research results（such as Stochastic Volatility（SV）model and SABR model）have the problem of solving complexity and difficult parameter estimation.In Carr and Wu（2016）（hereinafter referred to as the CW framework）,a new framework for volatility surface modeling is proposed,which makes the previous solving process relatively concise and efficient.Therefore,this paper also tries to expand the theory based on CW framework from various perspectives,and studies the 50ETF options of Shanghai Stock Exchange in China.Starting from static fitting of implicit volatility surface,this paper first uses polynomial fitting method,Heston model and SSVI model to statically fitting of implicit volatility surface of Shanghai 50ETF option,and compares the fitting effects of different models.Then,in the dynamic modeling part,we use two-step dynamic modeling based on polynomial and extended model based on CW framework to improve the implied volatility surface.By dynamic modeling,the time series diagram of model fitting parameters with rich economic meanings are obtained and compared with the prediction effect outside the sample.In addition,this paper also attempts to further expand and optimize the theoretical framework of CW from both theoretical and practical perspectives,and calibrate the model parameters with the help of Unscented Square Root Kalman Filter.Specifically,this paper first reviews the existing mainstream models of implied volatility surface modeling,focusing on the CW model framework,and on the basis of this framework,further explore the possible extension ideas mentioned in th eir papers.In this paper,we try to select the surface mean recovery assumption with implicit volatility as the parent model ip the framework.By comparing different polynomial two-step methods to predict the surface of volatility,we choose the best one as the submodel.Then we use the surface mean recovery term of the sub-model as the surface mean recovery term of the "parent model",and draw on the information of the two models by virtue of the advantages of the parent model in calculation.Complementary advantages,the proposed M-VGVV-J model not only improves the in-sample fitting effect,but also improves the prediction effect of out-of-sample model by comparing the original model.In addition,the model estimation method-Unscented Square Root Kalman Filter also improves the practical calculation performance of the theoretical model.In conclusion,based on the existing literature,this paper further demonstrates the theoretical scalability of CW framework and its potential great practical value.Finally,this paper utilizes VGVV,M-VGVV and M-VGVV-J models,based on empirical research of China SSE 50ETF options and US S＆P500 index futures options and finds that:1.For China SSE 50ETF options,both inside and outside the sample forecast,the introduction of predicted value of volatility surfaces and asset price jump can make the model fit and predict better than the original model;2.With the method of Square Root Unscented Kalman filtering,it can shows that the time series of different state variables,which fully reflect the model’s rich economic meanings;3.The robustness test of the model was conducted,and the performance of the US S＆P500 index futures options under different models was examined,and the same conclusions as before were obtained.