Optimal reinsuring of CDS contracts in OTC markets

Credit Default Swaps (CDSs) are derivative contracts thought to hedge the risk of a firm or the default of a bond. These contracts are based on interpersonal agreement without the supervision of an exchange. The valuation problem of CDS contracts in over-the-counter (OTC) markets is less studied mainly because the contracts are not standardized. To fill this gap, we provide a stochastic model for re-insuring CDS contracts in the OTC market. Applying a Markov chain credit rating model and dynamic programming techniques, we find the optimal reinsurance strategy over time which maximizes the insurer’s total discounted expected rewards. Changes to the value function are investigated according to a perturbation analysis of the model parameters. A numerical example illustrating the method of calculation is given in details.