Abstract
In this work, we introduce a general framework for incorporating stochastic recovery into structural models. The framework extends the approach to recovery modeling developed in Cohen and Costanzino (2015, 2017) and provides for a systematic way to include different recovery processes into a structural credit model. The key observation is a connection between the partial information gap between firm manager and the market that is captured via a distortion of the probability of default. This last feature is computed by what is essentially a Girsanov transformation and reflects untangling of the recovery process from the default probability. Our framework can be thought of as an extension of Ishizaka and Takaoka (2003) and, in the same spirit of their work, we provide several examples of the framework including bounded recovery and a jump-to-zero model. One of the nice features of our framework is that, given prices from any one-factor structural model, we provide a systematic way to compute corresponding prices with stochastic recovery. The framework also provides a way to analyze correlation between Probability of Default (PD) and Loss Given Default (LGD), and term structure of recovery rates.
Highlights
Background and MotivationIn his seminal paper, Wang (2002) proposed a transform method to price both liabilities and contingent claims, whether traded or not
One application of the Wang Transform is in option pricing, which for example can be used in the structural modeling of defaultable bonds
We present an analysis of the short-term credit risk in this Merton Model that we have extended to allow for the effect of jumps on the credit spread
Summary
Wang (2002) proposed a transform method to price both liabilities and contingent claims, whether traded or not. In the practice established by actuaries, the time value of money is another important aspect of bond pricing, and in the same issue that Wang’s paper appeared, Bühlmann (2002) proposed a paradigm shift in thinking about this technology. In his editorial, Bühlmann advocated that actuaries take a numeraire based approach to financial risk. A single factor for pricing such bonds assumes that bond and equity returns are perfectly correlated, which need not be true This leads to perfect correlation between probability of default and recovery-given-default, which is not empirically observed.
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