Partial hedging in credit markets with structured derivatives : a quantitative approach using put options

This study develops a novel method for mitigating credit risk through the use of structured derivatives, focusing in particular on the use of European put options as a strategic hedging tool. Inspired by the work of Merton (1974), our approach introduces the concept of default triggered by the stock price ST breaching a predefined barrier B. By establishing a distributional equivalence between an existing default model and P(ST<B) for a given time T, we demonstrate the potential for reducing the necessary capital allocation for a projected loss X(T) by partially hedging with a European put option. We formulate and solve an optimization problem w.r.t. a specific risk measure to determine the optimal strike price for the option, and our numerical analysis confirms a reduction in the Solvency Capital Requirement (SCR) in markets with and without jumps. Our findings provide (insurance) companies with a pragmatic approach to mitigating losses while maintaining their current risk management framework.