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研究生： 柯錫安
Shi-An Ko
論文名稱： 信用風險下可轉換公司債之評價
Pricing Convertible Bonds with Credit Risk
指導教授： 張森林
San-Lin Chung
口試委員:
學位類別： 碩士
Master
系所名稱： 管理學院 - 財務金融學系
Department of Finance
畢業學年度： 89
語文別： 中文
論文頁數： 42
中文關鍵詞： 信用風險 、可轉公司債 、模擬 、存續期間
外文關鍵詞： credit risk, convertible bonds, convertible, simulation, duration
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    • 除此之外，本文還利用Longstaff 和 Schwartz (2001) 提出的最小方差法來處理可轉換公司債本身的複雜特性，並針對公司價值波動性及可轉債所付票息的高低，對於可轉債的存續期間的影響進行研究。
    結果顯示，可轉換公司債的存續期間在某些條件下，將隨著所付票息的增加而增加


    study we use the model that was developed by Longsta_ and Schwartz (1995) to esti-
    mate the credit risk of convertible bonds. Moreover, the Least-Square-Method (LSM)
    proposed by Longsta_ and Schwartz (2001) is used to handle the hybrid features of
    convertible bonds. We also examine the e_ect of volatility on the value of convertible
    bonds and the duration of convertible bonds for di_erent parameters. The result shows
    that the value of convertible bonds may increase or decrease as the volatility of the
    firm''s value increases. The price of the convertible bonds is the result of a ombination of the debt part and the option part. Moreover, the duration of the convertible bonds,
    at low volatility, increases as the coupon rate increases when the other conditions are
    the same.

    Contents 1 Introduction and Motivation 1 1.1 Convertible Bond . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Credit Risk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.3 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2 Literature 3 2.1 Credit Risk Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.1.1 Firm Value Model . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.1.2 First Passage Time Model . . . . . . . . . . . . . . . . . . . . . 4 2.1.3 Intensity Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.2 Pricing Convertible Bonds . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.2.1 Finite Dierence and Lattice Method . . . . . . . . . . . . . . . 7 2.2.2 Monte Carlo Simulation . . . . . . . . . . . . . . . . . . . . . . 8 3 Notation, Assumption, and Algorithm 8 3.1 Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 3.1.1 The Conversion Condition . . . . . . . . . . . . . . . . . . . . . 10 3.1.2 The Call Condition . . . . . . . . . . . . . . . . . . . . . . . . . 12 3.1.3 The Put Condition . . . . . . . . . . . . . . . . . . . . . . . . . 12 3.1.4 The Maturity Condition . . . . . . . . . . . . . . . . . . . . . . 13 3.1.5 The Bankruptcy Condition . . . . . . . . . . . . . . . . . . . . . 13 3.2 Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 4 Result 21 4.1 The Price of Convertible Bonds . . . . . . . . . . . . . . . . . . . . . . 21 4.2 The Eect of the Volatility of the Firm''s Value . . . . . . . . . . . . . 22 4.3 The Duration of Convertible Bonds . . . . . . . . . . . . . . . . . . . . 24 4.4 Convexity of Convertible Bonds . . . . . . . . . . . . . . . . . . . . . . 29 5 Conclusion 30 A Appendix 33 List of Figures 1 The Value of Convertible Bonds, r 0 = 0:08, q = 18:52. . . . . . . . . . . . 23 2 The Value of Convertible Bonds at Dierent Initial Firm Values, r 0 = 0:08, q = 18:52. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 3 The Duration of a Straight Bond at Dierent Coupon Rates, V 0 = 50m, ˙V = 0:1, r 0 = 0:08, q = 18:52. . . . . . . . . . . . . . . . . . . . . . . . . 25 4 The Duration of Convertible Bonds at Dierent Coupon Rates, V 0 = 50m, ˙V = 0:1, r 0 = 0:08, q = 18:52. . . . . . . . . . . . . . . . . . . . . . . . . 25 5 The Duration of Convertible Bonds at Dierent Coupon Ratios, V 0 = 50m, ˙V = 0:7, q = 18:52, r 0 = 0:08. . . . . . . . . . . . . . . . . . . . . . . . . 26 6 The Duration of Convertible Bonds at Dierent Volatility and Coupon Rates, V 0 = 50m, q = 18:52, r 0 = 0:08. . . . . . . . . . . . . . . . . . . . . . . . 27 7 The Duration of Convertible Bonds at Dierent Coupon Ratios, V 0 = 50m, ˙V = 0:1, q = 18:52, r 0 = 0:08. . . . . . . . . . . . . . . . . . . . . . . . . 28 8 The Duration of Convertible Bonds at Dierent Initial Risk-Free Rates, V 0 = 50m, ˙V = 0:1, q = 18:52. . . . . . . . . . . . . . . . . . . . . . . . . . . 29 9 The Duration of Convertible Bonds with Dierent Features, V 0 = 50m, q = 18:52, ˙V = 0:2, r = 0:08. . . . . . . . . . . . . . . . . . . . . . . . . . . 30 10 The Convexity of Convertible Bonds at Dierent Volatility and Coupon Rates, V 0 = 50m, q = 18:52, r = 0:08. . . . . . . . . . . . . . . . . . . . . . . . . 31

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