Estimation of a Cox process for credit spreads with semi‐stochastic intensity

Purpose - The paper aims to present a framework for modeling defaultable securities and credit derivatives which allows for dependence between market risk factors and credit risk. Design/methodology/approach - The default event is modeled using the Cox process when the stochastic intensity represents the credit spread. A method of one‐sided risk approach is used in that default is modeled through a random intensity of the default time. Findings - The paper proposes a modified Cox model for defaultable interest rate term structure when the forward rate volatilities functions depend on time to maturity, on the instantaneous defaultable spot rate and on the entire forward curve. The Cox process describes the default event and its intensity denotes the credit spread. Research limitations/implications - A method of one‐sided risk approach sacrifices some generality. Recursive models are better to reach the latter. Practical implications - The main feature of the framework is that it reduces the technical issues of modeling credit risk to the same issues faced when modeling the ordinary term structure of interest rates. Results show a clear maturity‐dependent path. Originality/value - A main application of this model is pricing of claims in which the credit rating of the defaultable party enters explicitly. An implementation is given in a simple one factor model in which the affine structure gives closed form solutions.