混合模型下具有随机回收的可违约债券定价

摘要

This paper studies the pricing of a defaultable bond with stochastic recovery under the hybrid model. The pricing model with a negative correlation between the reco-very rate and the default intensity is sestablished by using the Ito’s formula and arbitrage-free principle. Then a closed-form solution to the pricing model is obt-ained by applying the variable transformation technique and partial differential equation (PDE) approach, which makes it convenient for portfolio management and hedging. Finally, numerical experiments are provided to illustrate the impact of recovery parameters and intensity parameters on the bond’s credit spread. The numerical results show that the credit spread under the stochastic recovery is lower than that of the corresponding fixed recovery, that is, the credit spread under the fixed recovery is overestimated.%本文研究混合模型下具有随机回收的可违约债券的定价。首先利用Ito公式和无套利原理建立了回收率与违约强度负相关的定价模型。然后，利用变量变换技巧和偏微分方程方法得到该定价模型的解析解，该解为投资组合管理和套期保值提供了方便。最后，通过一些数值算例分析回收参数和强度参数对可违约债券信用利差的影响。数值结果表明：考虑了随机回收风险的信用利差低于同等条件下固定回收的信用利差，即固定回收下的信用利差被高估。