Kijima, Masaaki and Katsuya Komoribayashi, "A Markov Chain Model for Valuing Credit Risk Derivatives", Journal of Derivatives, Vol. 6, No. 1, (Fall 1998), pp. 97-108.
Abstract: The credit derivatives market has grown rapidly, and the pricing of such a product requires credit risk information since credit derivatives are sensitive to a firm's credit quality. A recent paper by Jarrow, Lando and Turnbull (1997) proposed a Markov chain model for valuing risky debt that explicitly incorporates a firm's credit rating as an indicator of the likelihood of default. However, when applying the model to the actual market, some numerical problems arise from the fact that highly rated bonds have small default probabilities within the unit of time, say one year. This article proposes new risk premia adjustments to overcome this drawback. Extensive numerical experiments show that our model works well and is robust with respect to the recovery rate, especially for highly rated bonds, which is usually very difficult to estimate.