Time-varying copula models in the shipping derivatives market

In this paper, we provide an alternative hedging method based on a popular risk indicator relating to value at risk (VaR) for shipowners to hedge spot freight rate volatility in the tanker market. To achieve this, we use a univariate generalized autoregressive conditional heteroskedasticity model to capture the volatility characteristics of freight derivative returns and apply time-varying copula models to describe the nonlinear dependence between returns of spot and freight derivatives. Using quotes of spot freight rate and forward freight agreement (FFA) in the tanker market from January 3, 2006 to December 23, 2011, we derive the minimum VaR hedge ratios. Our main findings are as follows: First, we found significant evidence for the presence of volatility persistence in freight rate returns. Second, for dependence, we suggested that a time-varying t-copula performs best in describing how returns of spot freight rates relate to 1-month FFA returns, whereas a time-varying Gumbel copula performs much better for the description of nonlinear dependence between returns of spot freight rates and 2 and 3-month FFA returns. Third, the derived hedge ratios are associated with shipowners’ risk preferences and freight rate dynamics, which have important implications for shipowners in determining the optimal number of FFA contracts. The results provide some insights into the modeling of freight derivatives for risk management.