The aim of this paper is to analyse model risk within the context of credit risk modeling, and more specifically for defaultable bonds and credit derivatives. With the proliferation of financial losses related to the use of derivative securities risk management in general, and model risk management in particular has gained attention in the recent years. Recently, the booming credit risk literature has experienced a shift towards the so called reduced-form models that rely, basically, on an exogenous specification of default-inducing processes.
The reason is that these models are more amenable to empirical testing and, given suitable assumptions on recovery rates, allow straightforward application of the already available martingale pricing technology. In this vein, it is also easier to analyse market risk and credit risk together, which is crucial for versatile financial institutions operating in dynamic and intertwined environments.
The paper contributes to the credit risk literature in several ways. First, defaultable securities are priced in a framework that is unprecedented in its generality. Second, an extensive analysis of the effects, on valuation, of jump terms in both riskless interest rates and credit spreads is provided. Third, the influence of correlation between riskless interest rates and credit spreads is also analysed both from valuation, and hedging perspectives. Although jumps in interest rates recently have received some attention (see Akgun (2000) and references therein), the presence of jumps in credit spread dynamics has been so far ignored in both the empirical and theoretical literature.
As the distributions implied by observed credit spread dynamics are highly leptokurtic the relevance of incorporating jumps into the analysis becomes clear. There has also been a relatively higher but mostly qualitative interest in the correlation between market and credit risks, especially from a risk measurement perspective. The analysis in this paper, specifically sets out to quantify the effects of this correlation in pricing and hedging several defaultable securities. The framework of the paper is basically as follows. There are three state variables following jump-diffusion processes. The diffusion part is of CIR (1985) type. The risk less short-rate and the credit spread are affine functions of the state variables. There are three types of jumps. Jumps unique to the interest rate, jumps pertaining to the credit spread, and jumps common to both processes with a joint jump-size distribution depending only on time.