信用風險下可轉換公司債之評價

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姓名

柯錫安(Shi-An Ko ) 查詢紙本館藏

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財務管理研究所

論文名稱

信用風險下可轉換公司債之評價
(Pricing Convertible Bonds with Credit Risk)

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摘要(中)

信用風險在評價可轉公司債的過程中扮演非常重要的角色。在本論文中，我們利用Longstaff 和 Schwartz (1995) 提出的信用風險模型來評估可轉換公司債的信用風險。
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

摘要(英)

Credit risk plays a very important role in the valuation of convertible bonds. In this
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.

關鍵字(中)

★ 信用風險
★ 可轉公司債
★ 存續期間
★ 模擬

關鍵字(英)

★ convertible
★ convertible bonds
★ credit risk
★ duration
★ simulation

論文目次

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

參考文獻

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指導教授

張森林(San-Lin Chung)

審核日期

2001-6-28

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