Optimal Weak Static Hedging of Equity and Credit Risk Using Derivatives

We develop a generic method for constructing a weak static minimum variance hedge for a wide range of derivatives that may involve optimal exercise features or contingent cash flow streams to provide a hedge along a sequence of future hedging dates. The optimal hedge is constructed using a portfolio of pre-selected hedge instruments, which could be derivatives with different maturities. The hedge portfolio is weakly static in that it is initiated at time zero, does not involve intermediate re-balancing, but hedges may be gradually unwound over time. We study the static hedging of a convertible bond to demonstrate the method by an example that involves equity and credit risk. We investigate the robustness of the hedge performance with respect to parameter and model risk by numerical experiments.