Hedging Of Stock Index Futures With LPM Based On Copula-SV Model

One of the most important functions of hedging in future market is torealize the stock risk transfer。Stock index future provides a more flexibleportfolio management approach for institutional and individual investors toavoid spot assets risks. In this Paper, we work on how to calculate theproper hedging ratio in order to offer some useful advises to investors.Firstly we review four widely used hedging risk measures: variance,VaR, ES and lower partial moment (LPM). According to the characteristicsof hedging, we think LPM as the most suitable measure. But in practice,the difficulty lies in the determination of the joint distribution of the futuresand spots. In1959, Sklar proposed a tool to estimate the joint distribution,Copula function, which can decompose a joint distribution into k marginaldistributions and a Copula function, and the latter one describes thecorrelations between variables. In this paper, we choose LPM as the criteriaand build a Copula-based model to calculate the optimal ratio of hedgingbetween stock futures and spots. The CSI300stock index futures and the Shanghai and Shenzhen300index spot are selected as the research object. For the first step, we usethree techniques, GARCH, EGARCH and SV, to fit the marginaldistributions of returns of stock index futures and spots. By doing achi-square test separately on the standard residual sequence of their fittingswe found that SV-T describes the marginal distributions of return better.Step two, we consider to estimate the joint distribution utilizing fivecommon binary Copula functions. Also due to chi-square tests, a t-Copulafunction is picked out. Step three is to combine the selected SV-T andt-Copula function and add them into the application of calculating theLPM-based optimal hedging ratio. In order to better study the Copulamethod to calculate the LPM hedge ratio advantages and disadvantages,this paper calculated in different target rate of return and order numberusing Copula method to get the optimal hedge ratio value, in order tocontrast effect at the same time it gives two kinds of nonparametric methodof optimal hedging ratios the results. The last step is that we apply ourLPM ratio to another set of samples and compute their indices of H and R/SV to see if it really works well. The results show that Copula has asignificant advantage and is an approach conforming to real status.