Estimating And Using Non-gaussian GARCH Models With VIX Data For Hedging Schemes

With the rapid development of financial markets,the research of the options,futures and other derivative financial instruments research have become particularly important.Options as the core of the financial deriva-tives,is also a focus and hotspot in the research of the theory.In order to avoid risk,many scholars have been studying them from the two angles of option pricing and hedging.In this paper,when asset returns are modeled using a general class of non-Gaussian GARCH models,we put the informa-tion on VIX into the parameter estimation of the non-Gaussian GARCH model to improve the precision of estimated parameter.Moreover,we apply the VIX information data source as the initial volatility into the local risk minimization hedging to reduce the hedge error.Because the information on VIX under the risk neutral measures is more accurate,so we have put forward to consider local risk minimization hedging with different initial volatility under the extended Girsanov principle.In the end,a detailed nu-merical analysis based on S&P 500 European call option,returns data and VIX data is provided to assess the empirical performance of the proposed schemes.