Pricing Corporate Bonds with Interest Rates Following Double Square-Root Process

Chi-Fai Lo, C. H. Hui
2016 Social Science Research Network  
This paper develops a corporate bond pricing model following the structural approach in which the dynamics of the instantaneous risk-free interest rate are governed by a double square-root (DSR) process. Credit spreads generated from this pricing model depend explicitly upon the levels of interest rates via a nonlinear effect arising from a DSR process. Given a positive correlation between interest rates and leverage ratios, the credit spreads generated by this pricing model have a negative
more » ... tionship with interest rates, that is consistent with empirical findings using bond market data over the period 2008-2013 when interest rates were low. ratio (i.e., leverage ratio) will decline exponentially over time. In addition to the asset side, the Colin-Dufresne and Goldstein model specifies the drift of a mean-reverting default barrier (i.e., a firm's liability) to be a decreasing function of interest rates, which amplifies the static effect of interest rates on the leverage ratio. Kim et al. (1993) propose a pricing model that incorporates the CIR model for interest rates following a mean-reverting square-root process. One unresolved issue arising from the use of the CIR and Vasicek models is the relation between risk-free interest rates and credit spreads. Due to the specifications in the structural models proposed by Shimko et al. (1993) , Kim et al. (1993) , Schwartz (1995), and Colin-Dufresne and in which a firm's asset value is drifted by risk-free interest rates, these models predict a negative relation between risk-free interest rates and credit spreads. However, the specification of the asset value being drifted by interest rates also predicts that the expected leverage ratio will decline exponentially over time. The decline in the expected leverage ratio is however not supported by empirical observations.
doi:10.2139/ssrn.2797982 fatcat:walsp3rmerdtddcrb4yjpsr4qm