The pricing of defaultable bonds under a regime-switching jump-diffusion model with stochastic default barrier

ABSTRACT

In this paper, we investigate the price for the zero-coupon defaultable bond under a structural form credit risk with regime switching. We model the value of a firm and the default threshold by two dependent regime-switching jump-diffusion processes, in which the Markov chain represents the states of an economy. The price is associated with the Laplace transform of the first passage time and the expected discounted ratio of the firm value to the default threshold at default. Closed-form results used for calculating the price are derived when the jump sizes follow a regime-switching double exponential distribution. We present some numerical results for the price of the zero-coupon defaultable bond via Gaver-Stehfest algorithm.

KEYWORDS:

• Defaultable bond
• Jump-diffusion process
• Laplace transform
• Regime switching
• Stochastic default barrier.

MATHEMATICS SUBJECT CLASSIFICATION:

• 91B25
• 60J27
• 60G55

Acknowledgements

We thank an anonymous referee for the valuable comments which helped in improving the paper.

Additional information

Funding

The research was supported by the NSF of Jiangsu Province (Grant No. BK20170064), the NNSF of China (Grant No. 11771320), QingLan Project, the scholarship of Jiangsu Overseas Visiting Scholar Program and the Graduate Innovation Program (Grant No. KYCX17-2059) of Jiangsu Province of China.