Valuation of a loan-only credit default swap with negatively correlated default and prepayment intensities

Abstract

In this paper, we consider pricing of a single-name and a two-reference basket loan-only credit default swap. Under a reduced-form framework, it is assumed that the default and prepayment intensity rates for the reference loan, which are negatively correlated, follow one-factor Cox-Ingersoll-Ross (CIR) and inverse CIR models, respectively. The default and prepayment probability formulas are calculated using a partial differential equation method and closed-form solutions are obtained. A numerical analysis and the parameters are also discussed.