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

Son-Nan Chen, Pao-Peng Hsu and Chang-Yi Li

Quantitative Finance, 2016, vol. 16, issue 4, 573-592

Abstract: 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.

Date: 2016
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DOI: 10.1080/14697688.2015.1058520

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