不考慮交易對手違約風險下普通型、二元型、理想化型信用違約交換的評價

Abstract

信用違約交換是一種能轉移信用風險的衍生性金融商品。本文中我們證明了Hull and White (2000)文獻中的一個假設(在該文獻其它的假設之下)：公司債的現值等於無風險債券的現值減去違約所造成損失的現值。此外，在該文獻的基礎下，我們展示如何從債券價格推算出風險中立違約機率並利用其評價普通型及二元型信用違約交換。在我們的假設之下，我們也推導出二元型信用違約交換swap rate的一個上下界。最後，我們論述Hull and White (2000)文獻中的理想化型信用違約交換，並且在不同於該文獻的假設下定義另一個理想化型信用違約交換且評價之。在評價上述兩種理想化型信用違約交換時，我們不僅利用直接無套利論證推導並且利用適當的風險中立評價法驗證。

Credit default swap (CDS) is a financial derivative which can transfer credit risk from one party to another. In this thesis, we prove that the present value of a corporate bond is equal to the present value of the Treasury bond with the same payoffs minus the present value of loss by default, which is an assumption in Hull and White (2000). Following Hull and White, we also exhibit how to extract risk-neutral probabilities of default from bond prices and use them to value the swap rates of a plain-vanilla and a binary CDS. In addition, we derive an upper and a lower bound on the swap rate of a binary CDS under our assumptions. Furthermore, we detail the argument about the swap rate of an idealized CDS which is defined in Hull and White (2000). Moreover, we also define another idealized CDS in a different case and value its swap rate. In both case, we use both direct arbitrage arguments and also the appropriate risk-neutral pricing formula.