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 S T breaching a predefined barrier B . By establishing a distributional equivalence between an existing default model and <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"><m:mi mathvariant="double-struck">P</m:mi><m:mrow><m:mo>(</m:mo><m:mrow><m:msub><m:mrow><m:mi>S</m:mi></m:mrow><m:mrow><m:mi>T</m:mi></m:mrow></m:msub><m:mo>&lt;</m:mo><m:mi>B</m:mi></m:mrow><m:mo>)</m:mo></m:mrow></m:math> 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.