Pricing credit-risky bonds and spread options modelling credit-spread term structures with two-dimensional Markov-modulated jump-diffusion

• Published in: Quantitative finance 2016-04, Vol.16 (4), p.573-592
• Main Authors: Chen, Son-Nan, Hsu, Pao-Peng, Li, Chang-Yi
• Format: Article
• Language: English
• Subjects: Bond markets; Business cycle; Business cycles; Credit spread; Markov analysis; Markov-modulated jump-diffusion model; Put & call options; Spread; Stock prices; Studies
• ISSN: 1469-7688; 1469-7696
• DOI: 10.1080/14697688.2015.1058520

The relationship between company hazard rates and the business cycle becomes more apparent after a financial crisis. To address this relationship, a regime-switching process with an intensity function is adopted in this paper. In addition, the dynamics of both interest rates and asset values are modelled with a Markov-modulated jump-diffusion model, and a 2-factor hazard rate model is also considered. Based on this more suitable model setting, a closed-form model of pricing risky bonds is derived. The difference in yield between a risky bond and risk-free zero coupon bond is used to model a term structure of credit spreads (CSs) from which a closed-form pricing model of a call option on CSs is obtained. In addition, the degree to which the explicit regime shift affects CSs and credit-risky bond prices is numerically examined using three forward-rate functions under various business-cycle patterns.