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1、報告者：陳博宇,隨機利率下風險模型之衡量,探討架構,I.Longstaff&Schwartz,II.鍾明章,III.xtension,Francis A.Longstaff,Eduardo S.Schwartz,I.A Simple Approach to Valuing Risky Fixed and Floating Rate Debt,1,1.Introduction,2.The Model,3.Empirical Analysis,4.Concluding,Introduction,The articles developed a simple approach to valuing
2、risky corporate debt that incorporates both default and interest risk.The model provides a number of interesting new insights about pricing and hedging corporate debt securities.,The Model-Assumption,（1）,（2）,The Model-Assumption,5.If a reorganization occurs during the life of a security,the security
3、 holder receives 1-w times the face value of the security at maturity.6.We assume perfect,frictionless markets in which securities trade in continuous time.,The Model-Assumption,（3）,（4）,等式(3)的推導,等式(3)的推導,By Ito lemma,等式(3)的推導,等式(3)的推導,Vasicek 零息債券價格推導,Vasicek 零息債券價格推導,Vasicek 零息債券價格推導,The Model-Valu
4、ing,Fixed-rate debtFloating-rate debt 目前我們只討論fixed-rate debt的評價,因為Floating-rate debt對利率較不敏感,The Model-Valuing Fixed-Rate Debt,無風險的零息債券Vasicek的D(r,T),By Fubinis Theorem,By Buonocore,Nobile,and Ricciardi(1987),1.(R的影響),2.用X作為違約指標,.不同的對credit spread的影響,.R的credit spread的影響,.對credit spread的影響,.對credit sp
5、read的影響,Empirical Analysis,Concluding,1.The approach can be applied directly to value risky debt when there are many coupon payment dates or when the capital structure of the firm is very complex.2.The important insightsCorrelation of a firms assets with changes in the level of the interest rate can
6、 have significant effect on the value of risky fixed income securities.The term structure of credit spreads can have a variety of different shapes.,3.Empirical result Credit spreads are negatively related to the level of interest rates.Difference in credit spreads across industries and sectors appea
7、r to be related to difference in correlations between equity returns and changes in the interest rate.,鐘明璋,隨機利率下信用風險之衡量使用創新之立體樹狀模型,1.目的,2.方法,3.比較,目的,運用正交化的方法簡化資產和利率的聯合機率運算運用樹狀架構的數值方法求出有違約風險的公司債券價值近似解利用信用利差來觀察利率與公司信用風險之間的關聯,非線性誤差,非線性誤差是選擇權價值函數所引起的。門檻選擇權的報酬函數是根據在到期日公司資產有無碰到門檻值而定。,Stair Tree,方法,運用正交化的方
8、法將具有相關性的公司價值和隨機利率轉換成彼此獨立的新變數運用新變數建造數值樹狀模型資產部位：BTT Tree利率部位：二元樹並將二獨立的隨機變數的機率相乘，求得聯合機率計算其資產與利率的價值，最後導出其風險性債券的期初價值，並計算出其信用風險溢酬（credit spread）,正交化,公司資產標GMB:利率Vasicek:其中，與 獨立,正交化,將利率和資產表示成矩陣形式並試找到來正交化資產與利率,示意圖,：BTT tree,Y:二元樹,示意圖,利用樹狀結構的選擇權評價方法可求出具有違約風險的債券價值另外經由 求出風險利差，就可以觀察其信用風險與其相關因子的關係。,與Longstaff&Sch
9、wartz的模型比較,X,與Longstaff&Schwartz的模型比較,W,與Longstaff&Schwartz的模型比較,R,與Longstaff&Schwartz的模型比較,與Longstaff&Schwartz的模型比較,與Longstaff&Schwartz的模型比較,多討論公司資產發生jump的情況,與Longstaff&Schwartz的模型比較,多討論稅盾的影響,陳博宇,隨機利率下信用風險之衡量使用Hull-White Model,目前的想法,鐘明璋（2007）EDFPM的隨機利率是運用Vasicek model下的二元樹去模擬。運用Hull-White model(no-arbitrage model)的二階段三元樹去模擬。建構出立體二維樹後，求出信用風險溢酬與其經濟參數做比較。參照Eric Briys&Francois de Varenne(1997)所定的隨機threshold運用實驗方法去支持發現的論點,Thank for your attention,
