Relfected CEV Model And The Pricing Of Defaultable Bonds

In this paper, we are concerned with the default recovery risk in the pricing ofa zero-coupon defaultable bond. The main idea to characterize the default recoveryrisk is to propose a class of two-sided refected constant-elasticity-of-variance (CEV)processes to describe the term structure of default recovery given default. Moreprecisely, we introduce two regulators to CEV process so that the values lie in [c,1],where0<c <1which is close to zero, since default recovery rate is always between0and1. The reason for considering CEV processes here is that several popularterm structure models such as O-U, CIR, GBM can be covered by CEV case.Under the above proposed refected CEV term structure of default recovery, wediscuss the explicit pricing of a zero-coupon defaultable bond with recovery schemeof market value. Using stochastic analysis techniques, the price function for the de-faultable bond is proved that it satisfes a class of partial diferential equations withNeumann boundary condition at refecting barriers of default recovery. By employ-ing the Sturm-Liouville theory, the closed-form of price function can be obtained interms of eigenvalues and eigenfunctions associated to CEV generator．Several im-portant examples such as refected geometric Brownian motions, refected Brownianmotions, refected Ornstein-Uhlenbeck processes and refected square-root processesare presented．At the end of the paper,we perform some numerical illustrations ofthe price function with respect to the default recovery rate and the default intensi-ty respectively when the default recovery rate is described as a refected Brownianmotion．...