A Research Of Stock Option Valuation Based On Dynamic Hedging

The modern option pricing theory has two development directions,one is based on the model,through the establishment of the arbitrage equation,deriving the differential equation,seeking the analytical or numerical solution of the equation?The other is starting from historical information,exploring historical price information,and determining future options by predicting the future value of factors that have a decisive influence on the option price.Now,research of model method has entered a more in-depth stage.Although some results have been achieved,model method faces difficulties in the popularization due to its difficulties in applying.Option pricing through the non-model approach,is gradually getting more attention.Firstly,this paper expatiates on the background and significance of the topic of research,analyzes the traditional model pricing method,introduces the basic method of non-model option pricing.Secondly,this paper introducer unit GARCH and multivariate GARCH models and their estimation methods,and illustrates the application of GARCH model in option pricing.The sample period spread from January 3,2000 to December 21,2016,By comparing the error terms,I compare the efficiency of the two valuation model,the VIX index estimated by the DCC-GARCH model and the actual volatility estimated by the ordinary GARCH model in the regular option pricing model.Based on previous scholars' research,the dynamic hedging relationship between implied volatility and actual volatility is modeled in this paper.Following this idea,this paper implements the DCC-GARCH with realized covariance.Two-stage quasi-maximum likelihood estimation method is used to estimate the parameters of realized DCC-GARCH model.In the first stage,we use the realized GARCH model instead of standard GARCH model,thus establishing a VIX-return-realized volatility model.Finally,the price forecast of S & P500 index option is shown.The result shows that implied volatility index and the S & P 500 return index yield has a significant negative correlation.High frequency covariance has a significant effect on the correlation between low frequency implied volatility and actual variance.It is necessary to add covariance to the model.Although the future VIX expected value provided by realized DCC-GARCH model is still less than actual VIX,it is superior to the standard GARCH model in terms of option pricing.