A Bottom-Up Dynamic Model of Portfolio Credit Risk with Stochastic Intensities and Random Recoveries

Abstract

In Bielecki et al. (2014a), the authors introduced a Markov copula model of portfolio credit risk where pricing and hedging can be done in a sound theoretical and practical way. Further theoretical backgrounds and practical details are developed in Bielecki et al. (2014b,c) where numerical illustrations assumed deterministic intensities and constant recoveries. In the present paper, we show how to incorporate stochastic default intensities and random recoveries in the bottom-up modeling framework of Bielecki et al. (2014a) while preserving numerical tractability. These two features are of primary importance for applications like CVA computations on credit derivatives (Assefa et al., 2011; Bielecki et al., 2012), as CVA is sensitive to the stochastic nature of credit spreads and random recoveries allow to achieve satisfactory calibration even for “badly behaved” data sets. This article is thus a complement to Bielecki et al. (2014a), Bielecki et al. (2014b) and Bielecki et al. (2014c).

Keywords:

• Common shocks
• Markov copula model
• Portfolio credit risk
• Random recoveries
• Stochastic spreads

Mathematics Subject Classification:

• Primary 60J99, 91G40, 91B70
• Secondary 33F05, 91G60

Acknowledgments

We thank the anonymous referee for careful reading of the manuscript, for helpful comments, and for bringing to our attention important references.

Notes

Note that in this regard our CIR model is a special version of the segmented square root model of Schlögl and Schlögl (1997), where all three coefficients of the CIR diffusion are piecewise functions of time.

Color versions of one or more of the figures in the article can be found online at www.tandfonline.com/lsta.