The Study On Hedge Ratio Of China Stock Index Futures Based On GARCH Model

Stock index futures has been listed on April16,2010. Before that, the investorswere unable to avoid the systemic risk of the stock market. Stock index futures can helpinvestors to effectively avoid systemic risk, but its effect may be influenced by thehedge ratio. Thus, the key of hedging strategy is to determine the optimal hedge ratio.Firstly, in this thesis, the concept of hedging theory and the types of hedging theoryare summarized, and the risk minimization hedging strategy hedging ratio calculationformula is deduced. Then the commonly used risk minimization hedging ratioestimation models and their hedging ratio calculation formula are analogized.Secondly, in this thesis, the GARCH model is introduced from the initial elementGARCH model to a variety of complex multivariate GARCH model and the parameterestimation process of initial element GARCH mode is deduced. And the study mainlyfocuses on the BEKK model under the minimum variance hedging resale value formula.By analyzing the key statistical characteristics of Shanghai-Shenzhen300Index and thelogarithmic profits sequence of daily end-price of the stock index futures along withempirical experimenting using QQ graph, it is observed that the logarithmic price profitratio can be well fit by t distribution. Basing on it, the thesis makes a furthermodification to the BEKK-GARCH and multiple diagonal BEKK-GARCH models andthus constructs well-fit t distribution-based multiple BEKK-GARCH and multiplediagonal BEKK-GARCH models. In addition, the thesis derives the formula to computethe hedge ratio in the frame of the least portfolio profit risk.The last, parameters of the four models are estimated and the optimal hedge ratiosfor the models are calculated. The performances of the four models are compared. The empirical result shows that, based on comparing the performances of the four models,the hedging performance of the t distribution residual error-based diagonal BEKKGARCH model is the best, whilst BEKK-GARCH model is the worst. Overall, thehedging performance of the t distribution-based multiple BEKK-GARCH andmultiple diagonal BEKK-GARCH models is better than corresponding residual errorfollowing normal distribution.