A Copula-based Quantile Risk Measure Approach to Hedging under Regime Switching
In this thesis, our work builds on the future hedging strategy presented by Barbi and Romagnoli (2014). The authors propose the optimal hedge ratio as the minimizer of a generic quantile risk measure (QRM), which includes Value-at-Risk (VaR) and Expected Shortfall (ES). Moreover, the quantiles of the hedged portfolio can be represented in terms of a copula function, so that the dependence structure between the spot and futures could be better captured and hedging performance improved. In that paper, it has been shown that the empirical performance of the model is in general superior compared to some of the existing future hedging models that only consider limited risk measures or discard copula method. However, the model suggests that we use the static copula to fit observations during a previous long period and represent the spot-futures dependence structure. It may result in a poor representation as the dependence between the spot and futures is always characterized as time-varying. Moreover, as a consequence, it may yield a less accurate optimal hedge ratio and inefficient hedging performance. Motivated by this drawback, this thesis starts with the discussion of the robustness of the model in Barbi and Romagnoli (2014), where we use simulated data to conduct sensitivity analysis and performance test. Then an extension is proposed in which we allow the copula parameter to be dynamic and switch between different regimes. We consider two regimes and they correspond to relatively strong and weak dependence between the spot and futures return series. With such extension, we propose an hedging strategy to calculate the approximate optimal hedge ratio, which we call the extended regime-switching hedging strategy or the extended model. Monte Carlo simulations are followed to compare its new hedging performance with that of the original model without regime switching. The extended regime-switching model shows good advantage in capturing the dynamic dependence, but it dominates the original model in hedging effectiveness only when there are significant regime shifts in the spot-futures dependence and the difference of dependence level in two regimes is more dramatic. Finally, our proposed extended model methodology is applied to empirical data, where we use FTSE 100 stock index and its corresponding futures contract. The empirical results reconfirm our conclusions getting from simulated data.