General insurers frequently cede parts of their insurance risk to reinsurers in order to protect themselves from intolerably large losses in their insurance portfolio. This gives rise to a new type of risk, so-called reinsurance counterparty credit risk or RCCR that is the risk of a loss for the ceding company caused by the fact that the reinsurance company fails to honor her obligations from a reinsurance contract, for instance because the reinsurer defaults prior to maturity of the contract. Given the increased visibility of default risk in the reinsurance industry in the aftermath of the financial crisis, RCCR has become a highly relevant risk category, mainly because reinsurance recoveries represent large assets on insurance companies balance sheets. Nonetheless, the techniques for managing RCCR used in practice are mostly of a qualitative nature. Our objective is twofold: we discuss the computation of value adjustments to account for reinsurance default when pricing a contract, and we analyse dynamic hedging strategies in view of reducing the risk exposure. We consider a setting that is tailored to the analysis of RCCR. We model the aggregate claim amount process underlying the reinsurance contract under consideration by a doubly stochastic compound Poisson process. To capture the effect that “reinsurance companies are most likely to default in times of market stress, that is exactly when cedants are most reliant upon their reinsurance covers” (Flower et al. [3]), we introduce several sources of dependence between the aggregate claim amount and the default process of the reinsurance company. There is positive correlation between the claim arrival intensity and the default intensity of the reinsurer, and the claim arrival intensity exhibits a contagious jump at the default time of the reinsurer. In line with the concept of market consistent valuation we define the credit value adjustment (CVA) for an reinsurance contract as the expected discounted value of the replacement cost for the contract incurred by the insurer at the default time. Using results from the companion paper Colaneri and Frey [2], we characterize the CVA as classical solution of an integro partial differential equation. We address the hedging of RCCR by dynamic trading in a credit default swap. Here we resort to a quadratic hedging approach (Schweizer [1]) since perfect replication is typically not possible.
[1] Schweizer, M. (2001), “A Guided Tour through Quadratic Hedging Approaches.” Option Pricing, Interest Rates and Risk Management, pp. 538-574, Cambridge University Press.
[2] Colaneri, K., Frey, R. (2019), “Classical solutions of the backward PIDE for a Markov point process with characteristics modulated by a jump diffusion.” working paper.
[3] Flower, M. et al. (2007) “Reinsurance counterparty credit risks: Practical Suggestions For Pricing, Reserving and Capital Modelling.” 2007 GIRO RCCR Working Party, Institute and Faculty of Actuaries.