Extension And Empirical Applications Of Optimal Dynamic Hedging Method Option Pricing Theory Under Discrete Time

As one of the greatest inventions in financial fields,options have a long developing history.The growth and flourish of US option trading has giving an exemplary role for other countries.China’s option market also has rapid development.Based on the unique functions and market needs,options trading in the field or over-the-counter has attracted wide attention and anticipation.Therefore,the study of options’pricing and hedging is very important.Since its birth,B-S-M option pricing theory has a profound implication for the real stocks exchange.Without doubt it is a revolutionary success in option research fields.However,it’s not perfect because its assumption of complete and dynamics market is not in line with the reality.It is impossible to achieve complete hedging because of the incompleteness of the market.Therefore,it is particularly important to study the hedging methods in incomplete markets.Our paper studies the discrete-time hedging method in incomplete market.Based on the optimal discrete-time hedging method deduced from Basak and Chabakauri(2012)by minimizing the variance of hedging errors,and further consideration of the stochastic volatility,we derive the optimal dynamic hedging method and option pricing formulas.By simulation,we show the model derived by us can better describe the volatility smile and the moment risk premium than that of Basak and Chabakauri(2012),that is,it is closer to the real market situation.In the empirical analysis part,we choose the relevant data of the S&P 500 index and its corresponding call options with a one-month period as the sample data.Firstly,we estimate the model parameters.Then the exogenous variables,μ and σ,are calculated based on the results of parameter estimation,and added into the conditional variance equation of GARCH and EG ARCH model through different methods.By comparing the results of each model,we analyze the explanatory power of the exogenous variables having to the yield series.Besides,we analyze the prediction ability of μ and σ to Economic Policy Uncertainty index.