Modeling of CPDOs – Identifying optimal and implied leverage

When the subprime crisis started to emerge, collateralized products based on credit default swap (CDS) exposures combined with security features seemed to be a more rational alternative to classic asset backed securities. Constant Proportion Collateralized Debt Obligations (CPDOs) are a mixture of Collateralized Debt Obligations (CDOs) and CPPIs with inverse mechanism. This new asset aims at meeting the investors’ demand for credit derivatives with security enhancements, but to our knowledge quantitative approaches for pricing other than simulation algorithms do not exist yet. CPDOs became famous notably by Standard & Poor’s rating model error which illustrated that closed-form analytical pricing is necessary in order to evaluate and understand complex derivatives. This article aims to shed a light on CPDOs’ specific structural enhancements and mechanisms. We quantify inherent risks and provide a dynamic closed-form pricing formula.