Credit/Interest Rate Hybrid Models of the Short Rate for Pricing Counterparty Risk Adjustment

Abstract

This study is concerned with hybrid models of multiple stochastic processes and their use in pricing instruments whose payoffs depend on credit and interest rate variables. We introduce such a model and extend to two-factor modelling in both credit and interest rate dimensions, in order to relax the assumption of perfect correlation between survival probabilities of different tenors. We also assume that short interest and hazard rates evolve as correlated stochastic processes and apply simulation methods for pricing interest rate and credit default swaps with counterparty risk. Analytical CDS pricing formulas that consider the filtration of the simulated variables are also derived to significantly improve computational efficiency in the calibration and pricing procedures. Our numerical experiments indicate that the volatility of interest and hazard rates are significant parameters for the value of counterparty risk adjustment, while the correlation between survival probabilities with different time horizons are found to be far from perfect. These results strongly support the use of two-factor dynamic models.