Modelling The Option Expected Volatility Of Chinese Stock Market

The financial options,one of the most important financial instruments which play a very important role used as an efficient vehicle for risk management,arbitrage trading and so on,nowadays are becoming more and more popular in Chinese financial markets,too.By so far,there are only 7 exehange trade options available in entire Chinese markets,the corresponding underlying assets are 1)SSE50 index ETF;2)sugar;3)cotton;4)soy bean;5)corn;6)copper;and 7)nature rubber,respectively.The movement of options’ trading prices essentially reflect the mechanism for volatility surface efficiently,and keeping the implied volatility consistent with the volatility surface reflected by exchange trade options’market prices information is critical for the valuation of financial derivatives with embedded options(such as convertible bonds/dets,exotic options,or options embedded in fixed income security).However,there is no any exchange trade option on a single stock in Chinese Stock market,thus there is no any implied volatility surface available,and this is the main reason for us to work on the study of option expeeted volatility to construct the volatility surface(based on "Shanghai-Shenzhen 300 index")of options for the Chinese stock markets.In order to construct the volatility surface(based on "Shanghai-Shenzhen 300 index")of options for the Chinese stock markets,we apply a new method to model the volatility surface without using option price information,and the key idea of this is new method is based on the Black-Scholes-Merton(BSM)option model incorporating with the mechanism of Delta hedging(used in the practice of financial industry)which is capable of drawing out the volatility surface behind historical underlying path from the real markets,and we define this volatility surface as Option Realized Volatility Surface.Then we apply the GARCH(1,1)model to forecast the volatility of underlying assets’ return in near future terms to simulate the underlying paths for their price movements in the future.Finally,we compute the"Option Realized Volatility" based on each simulate path of underlying assets to construct the Expectation of Option Realized Volatility,which can be used as the "Option Expected Volatility Surface" for financial derivatives with embed options from Chinese stock markets.In order to test how good the method used for the construction of the "Volatility Surface",based on "Shanghai-Shenzhen 300 index"(in 2018),we calculate its Option Expected Volatility Surface and Option Realized Volatility Surface to conduct the numerical comparison.The results show that the Option Expected Volatility Surface generated by our method discussed in this search is efficient to model the Volatility Surface of underlying(without options derivative available)based on market information.