A credit contingent interest rate swap is an option that grants its holder the right, but not the obligation, to enter into an interest rate swap (IRS) at the time when its reference obligor defaults. The premium to be paid on the underlying IRS is fixed in advance at some strike level. The notional amount of the swap is a function of a predetermined fixed amount and the recovery rate of the reference obligor. The model can also be employed to back out an implied correlation between the interest rate and the default arrival of an obligor
The correlation between the swap rate and the hazard rate of an obligor is not a market observable and should be implied from the CCIRS market. For an obligor whose market implied correlation information can not be found, a historical analysis has to be used to obtain a reasonable estimate and a pertinent reserve has to be set up. A reserve methodology has been proposed by GRMMR London to address parameter uncertainties and approximations in the model.
The credit contingent interest rate swap (CCIRS or CCDS) valuation model serves the purpose of pricing an option that grants its holder the right, but not the obligation, to enter into an interest rate swap (IRS) at the time when its reference obligor defaults. The premium to be paid on the underlying IRS is fixed in advance at some strike level. The notional amount of the swap is dependent on a predetermined fixed amount and the recovery rate of the reference obligor.
In essence, a CCIRS trade can be regarded as an interest rate swaption with two special features. One is that the maturity of the swaption is the default time of the reference obligor, which is unknown. The other feature is that, although the strike of the underlying swap is predetermined, the tenor and the notional amount of the underlying swap are dependent on the default time and recovery rate of the reference obligor, respectively. The trade provides a hedging of the counterparty risk in an IRS.
The pricing and risk management of CCIRS trades depends on correlation between the default arrival of the reference obligor and the market value of the underlying IRS. For this reason, it is necessary to model the correlation, which can only be achieved by modeling the dynamics of the interest rate and the credit. The dynamic model of interest rates has been well established. Following the same methodology as that of interest rate modeling, people have also tried to model the default arrival via dynamics of either credit spreads or hazard rates. There have been several attempts to model the correlation between interest rates and credit.
The model is a simplified closed form solution, in which the swap rate dynamics are modeled as a lognormal process and the hazard rate dynamics are modeled as an Ornstein-Uhlenbeck (OU) process. Both processes are one-factor model and they couple to each other in a standard fashion. Although the model is simple compared with other proposed models, the apparent advantage of the model is that the basic instruments in a CCIRS trade, namely the swaption and the CDS, can be priced correctly. The effect of correlation between interest rates and credit can be explicitly quantified with known reasonable approximations.
Like all interest rate dynamic modeling approaches, the CCIRS model involves many parameters which should be calibrated to the pertinent market information. In the pricing of an interest rate swaption Black volatilities are calculated via a stochastic volatility model (SABR model), which is an approved model for the volatility skews and smiles. The default probability of the reference obligor is calibrated to the credit default swap (CDS) market and the volatility of the hazard rate is implied by the market information of the CDS option (CDSO).
The Correlation between interest rates and hazard rates can only be observed from the market information of the CCIRS itself. Therefore, apart from pricing, the model can be employed to back out the implied correlation. For an obligor whose market implied correlation information can not be found, a historical analysis has to be used to find a reasonable estimate and a pertinent reserve has to be set up. A procedure for determining a reserve has also been proposed by GRMMR London to address the uncertainties of the parameters and the approximations in the model.
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