A General Framework for Incorporating Stochastic Recovery in Structural Models of Credit Risk

Abstract

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 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.

Structural estimation of counterparty credit risk under recovery risk

“…As pointed out in Szegö (2002) , current market conditions call for the need for a complex and thorough modeling set-ups to provide proper support to the regulators for the design of quantitative policies. However, most of the previous works have separated the study of the CCR ( Brigo and Tarenghi, 2005 ;Brigo and Bakkar, 2009;Lipton and Sepp, 2009;Bielecki et al, 2011;Arora et al, 2012;Albanese et al, 2013;Brigo et al, 2013;Ballotta and Fusai, 2015;Bo and Capponi, 2015;Kim and Leung, 2016;Cohen and Costanzino, 2017;Ballotta et al, 2019;Li and Zhang, 2019 ) to that of stochastic recovery rates ( Chiang and Tsai, 2010;Amraoui et al, 2012;Schläfer and Uhrig-Homburg, 2014 ).…”