A reduced‐form model for pricing defaultable bonds and credit default swaps with stochastic recovery

Abstract

This paper presents a reduced-form model for pricing defaultable bonds and credit default swaps (CDSs) with stochastic recovery, where the recovery risk is coupled with the default intensity, while the default intensity is described by a stochastic differential equation. Closed-form pricing formulae for defaultable bonds and CDSs are obtained by applying variable change techniques and partial differential equation approaches. The closed-form pricing formulae can provide valuable assistance in analyzing certain complications associated with portfolio management and hedging analysis. Finally, numerical experiments are provided to illustrate how the recovery parameters and intensity parameters affect the credit spread of a defaultable bond and the swap premium of a CDS. Appl. Stochastic Models Bus. Ind. 2016, 32 725-739 H t = 1 ⩽t is the point processes generated by only default time . Moreover, Q is a risk-neutral probability measure. For more details, we refer to Elliott et al. [23] and the reference therein. Under this probability space, our model assumptions are as follows: 726 Appl. Stochastic Models Bus. Ind. 2016, 32 725-739 J. PAN AND Q. XIAO e − (t) 2a 2 < 0. (b) If we let R 1 = 0 in Equation (5), then this stochastic recovery model degenerates into a constant recovery model, which exists in most studies.

A contagion process with self-exciting jumps in credit risk applications

“…We know that, in theory, the proposed intensity process can become negative with very small probability due to the term σdW (t). Nevertheless, the use of such process for default intensity is popular among both academicians and practitioners due to its analytical tractability (For reference, see[14,21,22,26]). Further, one can take σ = 0, if required, in order to avoid the possibility of negative values.…”