信用風險論文集

Abstract

在Jamshidian(1989)對利率選擇權評價研究中，作者闡述了遠期平賭測度的用處。本研究也將利用這個技巧，說明風險性債券的評價過程，並且將這個過程示範於兩個發表於Journal of Fixed Income期刊的模型。首先，本文證明Cathcart and El-Jahel(1998)的評價模型存在封閉公式解，這個結果取代了原來作者所使用的複雜數值方法。其次，本文說明Schmid and Zagst's (2000)模型中個四個微分方程式求解過程，可以使用三個微分方程式即可。上述的結果都是利用遠期平賭測度轉換技巧達成的。

The usefulness of the forward martingale measure has been demonstrated by Jamshidian (1989) in deriving a pricing formula for default-free bond options. By making use of this technique, this paper offers a greatly simplified approach to the valuation of defaultable bonds by revisiting two pioneering hybrid models published in the Journal of Fixed Income. First, Cathcart and El-Jahel's (1998) original numerical inversion of Laplace transformations for pricing defaultable bonds is replaced with a closed-form formula derived through the use of the forward martingale measure. Second, Schmid and Zagst's (2000) original four ordinary differential equations for pricing defaultable bonds are replaced by three ordinary differential equations via the use of the forward martingale measure again.