Bierwag [1987] 指出甚少有研究探討違約風險對於存續期間相關策略的影響，本研究探討在考慮違約風險與嵌入式選擇權下，兩種不同計算利率風險方法的差別。 Tzeng, Wang and Soo [2000] 提出一個新的免疫策略，可以獲得最大的凸性效益。我們延續這個策略，但是假設金融機構的資產負債表上的債券是有違約風險與嵌入式選擇權性質的。最後，我們舉一個例子說明凸性效益的重要性。 Bierwag [1987] points out that there has been very little research into the default effects on duration-based strategies. This study compares two duration measures for evaluating the interest rate risk of a non-default-free bond with embedded option properties. Tzeng, Wang, and Soo [2000] demonstrate that linear programming can implement a new optimal immunization strategy to maximize the convexity gain. We follow this strategy but assume the financial institution has non-default-free bonds with embedded options on their balance sheets. Further, we illustrate a example to show the importance of the convexity gain
