Pricing Credit Derivatives Under Fractional Stochastic Interest Rate Models with Jumps

Based on the reduced-form approach, this paper investigates the pricing problems of default-risk bonds and credit default swaps(CDSs) for a fractional stochastic interest rate model with jump under the framework of primary-secondary. Using properties of the quasi-martingale with respect to the fractional Brownian motion and the jump technique in Park(2008), the authors first derive the explicit pricing formula of defaultable bonds. Then, based on the newly obtained pricing formula of defaultable bonds, the CDS is priced by the arbitrage-free principle. This paper presents an extension of the primary-secondary framework in Jarrow and Yu(2001).