Comparing the reliability of a discrete-time and a continuous-time Markov chain model in determining credit risk

Abstract

This article compares the reliability of a discrete-time and a continuous-time Markov chain model for estimating credit risk and for investigating loans of Chiao Tung Bank in Taiwan. The continuous-time Markov chain model can capture the migration of rare events. The time-varying risk premium was also extracted from the loan value and corresponding risk-free price and the transition matrix was transferred to risk-neutral transition matrix by the time-varying risk premium. Finally, the empirical results indicate that the discrete-time Markov chain model may be underestimating the default probability in both the lowest risk and speculative rating class. Comparing the loss given default and the NPL ratio, the continuous-time Markov chain model is more reliable and effective for gauging the credit risk of bank loans.

Acknowledgements

The author thanks anonymous reviewers and the editor for their helpful recommendations. Financial support from the National Science Council (NSC 95-2416-H-239-004) is gratefully acknowledged.

Notes

¹ If there is no collateral or asset backing, then δ = 0.

² There are two approaches to gauge the risk premium, namely Jarrow et al. (1997) and Kijima and Komoribayashi (1998). However, Jarrow et al.’s procedure will cause the risk premium to explode. Consequently, Kijima and Komoribayashi's (1998) method was adopted to extract the risk premium, which is time-varying.

³ The NPL refers to loan accounts, the principle and/or interest of which are past due or exceed the due date. Therefore, the NPL ratio is NPL divided by the total loan portfolio. In this study, the NPL ratio was obtained from TEJ's database.

⁴ Since the NPL ratio was concerned, as loans were uncollected after all collection option, such as the realization of collateral or the institution of legal proceedings, has been exhausted.