Non-arbitrage Implied Volatility Surface Modeling And Option Pricing

As an important financial derivative,option is widely used in investment and risk management.Since China’s first exchange-traded option 50 ETF was listed on the Shanghai Stock Exchange on February 9,2015,both the floor market and the OTC market have achieved great development in terms of trading volume and product types.However,Chinese option market is still immature compared with overseas.Previous studies have pointed out that Chinese option market has low pricing efficiency and arbitrage opportunities.Implied volatility,as the key factor of option pricing,has long been an important subject of option pricing studies for both domestic and foreign scholars.At present,although the research on implied volatility surface modeling has made some progress in China,the research arbitrage opportunities has been neglected to some extent.Therefore,the study of non-arbitrage implied volatility model is of great significance to improve the low pricing efficiency and the problem of arbitrage in our options market.SVI model and eSSVI model have been widely used in overseas options market due to their explicit no arbitrage conditions and convenient parameter calibration methods.Based on the data of the 50 ETF option market,parameter calibration of the SVI model and eSSVI model is carried out in this paper.The results show that both models can correctly fit the implied volatility data in the market,and the implied volatility surface constructed by the e SSVI model can effectively eliminate static arbitrage opportunities.Based on the implied volatility surface constructed by e SSVI model,this paper constructs the local volatility surface with Dupire equation,and exams the pricing of European options with Monte Carlo simulation and finite difference method.The results show that the model used in this paper can accurately price the European options.The local volatility model constructed by e SSVI model can effectively connect the exchange traded market and the OTC market,enabling investors to conduct unified pricing,trading and hedging of options contracts on the two markets and ensuring that there is no static arbitrage opportunity for the quotation of different contracts.This paper provides a tool for domestic investors with volatility trading and risk management.To some extent,it will improve the low pricing efficiency and arbitrage opportunity phenomenon in options market in China,and further promote the development of options market in our country.