This paper first develops a reduced form three-factor model for valuing credit default premia that is used to provide implicit prices which are then compared with market prices of credit default swaps to determine if swap rates adequately reflects market risks. This model extends Jarrow (2001) two-factor model by adding three new features to enhance the effectiveness of the model and add to the growing debate on the empirical pricing of credit default swap and the effectiveness of reduce form models. Firstly, the extended model retains Jarrow's mean reverting properties but will be extended to be arbitrage free because of the use of a Cox-Ingersoll-Ross (CIR) process, thus improving the study's ability to estimate the no arbitrage value of the CDS premium. Secondly, a liquidity variable is added to the model to capture the level of liquidity in the market, which conjectively impacts CDS valuation. Thirdly, the model now makes use of an expanded dataset of 53 companies and 15 months of daily data, which should lead to more robust estimators.
The paper first develops the Jarrow (2001) two-factor mean reverting model of credit default swap valuation, with a constant recovery rate and a non-linear hazard function. Methodologies were then proposed for extending Jarrow's model to a three-factor model so as to improve the effectiveness of the model in pricing the study's short-term maturities. For the three-factor model the study assumed that CDS prices are a function of the spot rate of interest and CDS market liquidity. The study follows the assumption that default probabilities are implicit in the default swap prices and market and credit risks are correlated across companies and dependent on the state of the macro-economy.
The study derived a closed-form expression for CDS prices, and examines its implications for pricing under both the two-product and three-product methodologies. Both models were empirically tested using daily CDS pricing data from December 31, 2002 to July 25th 2003. In both models the parameters of the hazard function were estimated using non-linear regression. Finally, empirical evidence of the model's performance is presented.
Dunbar, Kwamie, "An Empirical Review of US Corporate Default Swap Valuation: The Implications of Functional Forms" (2005). WCOB Faculty Publications. 273.