利用兩維度Cox-Ingersoll-Ross模型分解公司債溢酬以高盛為例

Abstract

本文旨在延伸Lonstaff (2005) 公司債溢酬分解模型。藉由放寬信用風險溢酬與流動性溢籌彼此統計獨立的假設，本研究得以探討兩者互動的情形，然而放寬假設卻有可能使得公司債定價失去解析解，因此利用 Brigo and Alfonsi (2005) 提出的近似公式以逼近理論公司債。由於該模型涉及到的參數大多無法直接從市場觀察而來，這使得參數估計變得更加困難，因此本研究另外提供方法去推估合理的參數值區域，最後輔以實際例子供示範之用。

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.