隨機利率模型下，與物價指數連動並具有信用風險之票券的評價與避險

Valuation and Hedge of Inflation-linked Notes with Credit Risk under a Stochastic Interest Rate Model

本文提出一個與物價指數連動且具有信用風險的票券，並應用Cathcart & El－Jahel （1998）模型中的顯著變數法（Signaling Variable Method），在HJM模型下，推導該票券合理價格、避險參數和信用價差的封閉解。相較於傳統的抗通膨票券和信用風險模型，本模型具有以下之特色。第一，在Cathcart & El－Jahel（1998）模型中，顯著變數（signaling variable）與利率之間是彼此獨立（independent），而本模型放寬此假設，讓顯著變數與利率彼此相依（dependent），使模型更切實際。第二，本模型結合信用風險（credit risk）和通膨風險（inflation risk），在物價持續上揚之際，更能確保投資人期末的實質收益。第三，一般而言，當標的資產的波動度上升，票券的價格會隨之提高，但是本模型，同時存在通膨風險和信用風險，當資產的波動度和物價的波動度越大時，因信用風險溢酬和通膨風險溢酬隨之提高，致使票券之合理價格下降。第四，當物價指數的動態過程為隨機過程（stochastic process）時，本模型的標的資產如同浮動面額債券，因此本文之訂價方式，可應用於浮動面額債券之評價。

This article expands the work by Cathcart & El-Jahel (1998) to present a new design of inflation-linked defaultable notes. We derive a closed-form solution to the fair price, delta hedge and credit spread under the HJM model. These notes differ from traditional inflation-protected notes and defaultable models for several reasons. First, this model relaxes the assumption of independence of signaling variables and interest rates in the signaling variable approach presented by Cathcart & El-Jahel (1998). This relaxation can actually meet a real world. Second, the model incorporates credit risk and inflation risk, and it can prevent investors' real payoffs at maturity from inflation. Third, in general, the fair price of defaultable notes is higher as volatility of underlying assets increases. Conversely, the fair price in our model is lower when the volatility arises on account of higher credit risk premium and inflation risk premium. Fourth, the pricing procedure of this model can be applied to the valuation of floating-rate bonds.