Corporate Yield Spread Decomposition with two-dimensional Cox-Ingersoll-Ross Model and Goldman Sachs Case Study

This paper is primarily intended to generalize the framework of Longstaff (2005) by regarding the default intensity process and liquidity process a two-dimensional correlated CIR process. However, we may lose the analytically tractable solution of the defaultable bond with such modifications. Consequently, we implement a Gaussian dependence mapping proposed by Brigo and Alfonsi (2005). Besides, we provide a technique to sketch the possible region where parameters will fall in case of parameter identification problems. Finally, we offer a case study to illustrate those methods in practice.