A Study Of Volatility Surface Modeling Based On Arbitrage-free SVI

Implied volatility model has always been an important content of option pricing theory.After the outbreak of the US stock market crisis in 1987,the phenomenon "volatility smile" of option had an important impact on the development of option pricing theory.The non normal distribution of the underlying return on assets forms the skewness of the volatility smile,and the changes of the implied volatility with the same degree of value at different maturities are reflected in the term structure of the implied volatility.This skewness and the term structure of the implied volatility constitute the implied volatility surface.We summarize the development theories and latest achievements of options pricing models at home and abroad,and start with the theory of arbitrage-free pricing,deriving the necessary and sufficient conditions.We focused on introducing the non-arbitrage SSVI model to explore its effectiveness and applicability in the50 ETF option market.Due to the complexity of stochastic volatility model,we use two parametric models,SVI and SABR model,which are simple and relatively accurate in option pricing.On the one hand,it is to examine whether the model can accurately depict the skewness and term structure of the volatility surface,on the other hand,it is to examine the pricing robustness of the model.Firstly,we select the daily data of 50 ETF from 2021 to 2022,and calibrate the implied volatility curve under the presence of optimism and panic.We concluded that the SVI model has the smallest fitting error at both moments.The SSVI model loses some accuracy due to arbitrage-free pricing,but with a significant increase in calibration speed,and also maintain a small pricing error.The skewness and term structure of SSVI volatility surface can well reflect different market sentiment,and relize no static arbitrage at the same time.Secondly,we test the fitting error of the call option and the put option respectively in the uptrend,downtrend and the whole sample period,and conclude that in the full sample period,three models roughly show that the ITM options in the far month have smaller MAE,and the OTM options in the recent month have smaller RMSE,reflecting the robustness of the model.The SSVI model as a whole reflects the characteristic of overestimating option prices,with pricing errors generally between the SVI and SABR models.When there is sentiment in the market,SSVI has a better fitting effect on ATM options in far months.In the out of sample pricing,the overall pricing performance of the SSVI model is also better than SABR model,indicating the model did not lose much pricing accuracy due to the implementation of no arbitrage,and also has good pricing performance and prediction ability in the 50 ETF option market.The innovation points of this paper:(1)Introduce the arbitrage-free SSVI model into the 50 ETF option market,and examining whether the model will lose more accuracy when realizing arbitrage-free;(2)Investigate whether the SSVI volatility surface can reflect the current market sentiment,and study the pricing error during the optimism and pessimism.There are still some shortcomings:(1)We only use the parametric model for comparison,without some more theoretical significance models which can also achieve no arbitrage;(2)The term of the data set is not long enough,only uing lowfrequency data;(3)The market information extracted from the volatility surface is not enough;(4)The arbitrage-free pricing is not considered from a dynamic perspective.