Pricing a defaultable bond with a stochastic recovery rate

A closed-form formula for the analysis of defaultable bonds is essential for market practitioners and financial researchers. In order to make the model more reasonable without loss of generality, it is necessary to specify the stochastic processes of the default-free short interest rate, the default intensity rate, and the recovery rate as affine functions with multi-dimensional space of the correlated state variables within the models. However, the pricing procedure is more sophisticated when the model includes such specifications. The purpose of our study is to deal with the complicated pricing procedure by utilizing the concept of the moment-generating function and then to derive the closed-form solution of a defaultable bond. Furthermore, we provide an example to illustrate the application of our model and conduct sensitivity analyses of the bond value for changes in the parameters of our model. Our closed-form formula based on more realistic specifications not only enables one to appropriately price the defaultable bond, but also enables portfolio managers to undertake sophisticated portfolio management and hedging analyses.