Study of Dynamic Hedging Based on the Laplace Distribution Multivariate GARCH Model
|School||Zhejiang University of Finance|
|Keywords||minimum variance hedging DCC-MVGARCH model BEKK-MVGARCH model CCC-MVGARCH model multivariate Laplace distribution|
To avoid price risk has been a major function of futures market, its realization is mainly accomplished by hedging. Hedging in essence is that the hedgers use the basis of futures price and spot price to avoid spot asset price risk. Hedge ratio is the ratio of futures position size that hedgers hold and spot asset position size .Different hedging rate results in different hedging performance .Therefore, the determination of optimal hedge ratio always is the core problem in the study of hedging. The traditional hedging theory holds that the optimal hedge ratio constantly is 1, but in the actual hedging process, constant hedge ratio is not the optimal hedging strategy. Then the hedge ratio based on modern portfolio theory appeared. The study of hedging ratios based on modern portfolio theory can be divided into two categories, one is from the Angle of portfolio risk minimization, and another is from the perspective of the utility maximization based on considering as a whole portfolio return and variance, to study the optimal hedge ratio. In this paper, the optimal hedge ratio formula is developed based on the portfolio risk minimization.As the development of econometrics, plenty of financial time series model are developed. These econometric models are used to estimate the optimal hedge ratio, thus forming different hedging model. These hedging models can be divided into two types: one is static hedging strategies, such as OLS model, error correction model; another kind is the dynamic hedging strategies, such as GARCH model group, SV model group. As the financial market and the financial theory develop, the GARCH model is continuously researched and improved developed from an initial element GARCH model to a variety of complex multivariate GARCH model group. While the multivariate GARCH model development can be divided into two categories, one category is that the conditional variance and covariance matrix of multivariate GARCH model can be directly estimated such as BEKK model, the other is that the multivariate GARCH model is decomposed into the linear combination of a plurality of single variable GARCH model, so that the number of estimated parameters can be reduced, such as CCC-MVGARCH model and DCC-MVGARCH model.In this paper, in the framework of minimum variance hedging theory, we choose BEKK-MVGARCH model、DCC-MVGARG mode and CCC-MVGARCH model in the multivariate GARCH model group to estimate the optimal hedge ratio of cu ,based on the copper futures and spot price yield data of the Shanghai futures exchange .For the futures and spot daily price return series have the characteristics of spike tail ,the residuals of above three models are further improved, by changing the residual that was originally assumed following multivariate normal distribution for that following multivariate Laplace distribution. Then compare the hedging performance of the three models, as well as comparing the hedging performance of unimproved and improved the corresponding model. The empirical results show that: in the three models, the hedging performance of DCC-GARCH model is the best of the three models, BEKK-GARCH model was the worst. But for the three models, the hedging performance of residual following Laplace distribution is better than corresponding residual error following normal distribution.