Modeling the Recovery Rate in a Reduced Form Model

Abstract

This paper provides a model for the recovery rate process in a reduced form model. After default, a firm continues to operate, and the recovery rate is determined by the value of the firm's assets relative to its liabilities. The debt recovers a different magnitude depending upon whether or not the firm enters insolvency and bankruptcy. Although this recovery rate process is similar to that used in a structural model, the reduced form approach is maintained by utilizing information reduction in the sense of Guo, Jarrow, and Zeng. Our model is able to provide analytic expressions for a firm's default intensity, bankruptcy intensity, and zero-coupon bond prices both before and after default.

Information uncertainty related to marked random times and optimal investment

“…In this section, we consider an explicit example where the random default time τ is given by a hybrid model as in Campi et al (2009) and Carr and Linetsky (2006) and the information flow G is supposed to depend on the asset values at a horizon time which is similar to Guo et al (2009). Let B = (B t , t ≥ 0) be a standard Brownian motion and N P = N P t , t ≥ 0 be a Poisson process with intensity λ ∈ R + .…”

“…For example, in the credit risk analysis, modelling the recovery rate is a subtle task (see, e.g. Duffie and Singleton (2003) Section 6, Bakshi et al (2006), and Guo et al (2009)).…”

Recovery Process Model

“…The recovery rate is mainly determined by the collateral value at default in their paper. Guo et al (2008) introduce the random recovery rate in the reduced form model. The reduced form model focuses on modeling the stochastic process for the default intensity.…”

Distressed debt prices and recovery rate estimation

“…Let b E( ) denote our expectation of R t looking backwards in time, starting at 1 , using the information sets discussed above. Then, using expression (13) we obtain: b E (R t ) = R 1 e a( 1 t) + b(1 e a( 1 t) ) for t 1 :…”

“…For a paper describing the economics of the distressed debt market see Altman [2]. For a related paper modeling defaulted debt prices in a reduced form model see Guo, Jarrow, Zeng [13]. Guo, Jarrow and Zeng's model is more complex than the model implemented herein, and they provide no empirical estimation.…”