有違約風險的選擇權：對偶問題

Abstract

本文嘗試延伸有違約風險的選擇權評價公式，考慮在首次通過模型的前提下，推導有違約風險的選擇權之封閉解；以及其對偶問題：考慮在Merton結構式模型的前提下，推導有違約風險的障礙選擇權之封閉解。並且依照本文方法，利用有違約風險的選擇權之封閉解和 in-out parity性質，可延伸評價其他型態障礙選擇權。並將其延伸至結構型債券，如 Reverse exchangeable bond 和 Barrier reverse convertibles 的評價上。

This paper presents a method of pricing vulnerable vanilla options under the first passage model. Similar approach can be applied to solve the dual problem－pricing barrier options under the Merton’s structural model. By applying the closed-form solution of vulnerable barrier options and the in-out parity, we can derive other types of barrier options. Finally, our formulas can be used to evaluate structural notes, like reverse exchangeable bond and barrier reverse convertibles.