Hedging for multi-period downside risk in the presence of jump dynamics and conditional heteroskedasticity

Abstract

This study extends the one period zero-VaR (Value-at-Risk) hedge ratio proposed by Hung et al . (2005) to the multi-period case and incorporates the hedging horizon into the objective function under VaR framework. The multi-period zero-VaR hedge ratio has several advantages. First, compared to existing hedge ratios based on downside risk, it has an analytical solution and is simple to calculate. Second, compared to the traditional Minimum Variance (MV) hedge ratio, it considers expected return and remains optimal while the Martingale process is invalid. Thirdly, hedgers may elect an adequate hedging horizon and confidence level to reflect their level of risk aversion using the concept of VaR. Pondering the occurrence of volatility clustering and price jumps, this study utilizes the ARJI model to compute time-varying hedge ratios. Finally, both in-sample and out-of-sample hedging effectiveness between one-period hedge ratio and multi-period hedge ratio are evaluated for four hedging horizons and various levels of risk aversion. The empirical results indicate that hedgers wishing to hedge downside risk over long horizons should use the multi-period zero-VaR hedge ratios.