A Markov Chain Model for Valuing Credit Risk Derivatives

Measurement and Estimation of Credit Migration Matrices

“…The second question is addressed using resampling methods, and the third using two approaches: the first is to estimate by simulation the credit risk capital levels implied by the credit portfolio model in CreditMetrics™ which is used to generate value distributions of a portfolio of credit assets such as loans or bonds. The second is the pricing of a credit derivative called a credit yield spread using the pricing model of Kijima and Komoribayashi (1998).…”

“…This can range from an increase in value of 1-2% in case of upgrade to a decline in value of 30-50% in case of default, as illustrated in Table 1. 4 More sophisticated examples of risky bond pricing methods, such as outlined by Jarrow and Turnbull, (1995) and Jarrow, Lando and Turnbull, (1997), require these matrices as a cardinal input, as do credit derivatives such as the model by Kijima and Komoribayashi (1998). As a final example, credit portfolio models such as CreditMetrics™ (JP Morgan (1997)) used in risk management make use of this matrix to simulate the value distribution of a portfolio of credit assets.…”

Transition probability matrix methodology for incremental risk charge

“…The modeling approach with deterministic intensity approach by Lando [7], Jarrow, et al [8], and Kijima and Komoribayashi [9], and Lando [10] is highly relevant to the problem posted here. As discussed in [6] and shown in [9], all these adjustments are materially different and it is unclear which one performs the best, indicating that the modeling uncertainty is large. We implemented several of them and tried to highlight the difference of the resulting one-year TPM.…”

The Probability of Default Under IFRS 9: Multi-period Estimation and Macroeconomic Forecast

“…Popular applications included empirical studies of default risk and rating migrations of bonds (e.g. Altman, Kao, 1992;Carty, Fons, 1994), pricing of bonds and derivatives (Jarrow et al, 1997;Kijima, Komoribayashi, 1998), and credit portfolio valuation (Gupton et al, 1997). Since the beginning of the 21 th century, the range of applications of transition matrices has become even wider and transition matrices have become an integrated part of modern credit risk management.…”