臺灣博碩士論文加值系統

本論文以二項數建立可轉換公司債之評價模型，並加入破產風險的考量，其中破產機率藉由KMV公司所發展出的KMV模型預測。比較三種不同的破產機率假設下，所評價出的可轉換公司債價格，並且取樣五檔在美國發行之可轉換公司債，做實證分析，看評價模型考慮破產機率後，是否貼近市場價格。

This thesis combined the KMV model with the Binomial-tree model for pricing con-vertible bonds (CBs). The KMV model is a sort of structural models for credit risk to generate the Expected Default Frequency (or EDF). Some numerical examples are given to illustrate our model and others. Five zero-coupon CBs issued in the U.S. are collected to conduct the empirical studies to compare the results of our model and the real market price.

Contents
Contents I
List of Tables II
List of Figures III
1 Introduction 1
2 The Model 5
2.1 Prediction default probability-Moody’s KMV Model . . . . . . . . . . . . . 5
2.2 CB pricing model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.3 Our model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
3 Numerical Analysis 12
3.1 Default probabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
3.1.1 Stochastic default probability . . . . . . . . . . . . . . . . . . . . . 12
3.1.2 Constant default probabilities . . . . . . . . . . . . . . . . . . . . . 14
3.1.3 Without default . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
3.2 The values of CB under different default cases . . . . . . . . . . . . . . . . 15
3.2.1 The Volatility of Equity . . . . . . . . . . . . . . . . . . . . . . . . 16
3.2.2 The debt ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
4 Empirical Studies 19
4.1 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
4.2 The Empirical results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
5 Conclusion 23

List of Tables
Table 2-1 The Relationship of DD and EDF . . . . . . . . . . . . . . . . . . . . 7
Table 3-1 The Price of CB with Different Volatility of Equity. . . . . . . . . . . 16
Table 3-2 The Price of CB with Different Leverage of Firm. . . . . . . . . . . . 18
Table 4-1 The Growth Rate of Debt of HEWLETT-PACKARD. . . . . . . . . . 20
Table 4-2 The Information of the Contract of CB. . . . . . . . . . . . . . . . . 21
Table 4-2 (continue) The Information of the Contract of CB. . . . . . . . . . . 22
Table A.1 The Growth Rate of Debt of MARRIOTT. . . . . . . . . . . . . . . . 26
Table A.2 The Growth Rate of Debt of SHAW. . . . . . . . . . . . . . . . . . . 26
Table A.3 The Growth Rate of Debt of SOLECTRON. . . . . . . . . . . . . . . 27
Table A.4 The Growth Rate of Debt of CAMERON. . . . . . . . . . . . . . . . 27

List of Figures
Figure 2-1 The General Ideal of the Relationship of DD and EDF. . . . . . . . . 5
Figure 2-2 The One-Period Tree for the Simple CB Pricing Model. . . . . . . . . 8
Figure 2-3 The Payoff of Each Node. . . . . . . . . . . . . . . . . . . . . . . . . 8
Figure 2-4 DD as a Function of D/E Ratio. . . . . . . . . . . . . . . . . . . . . 10
Figure 2-5 DP as a Function of DD. . . . . . . . . . . . . . . . . . . . . . . . . . 10
Figure 2-6 The One-Period Tree for Our Model. . . . . . . . . . . . . . . . . . . 10
Figure 2-7 Four Elements at Each Node to Determine the Credit Risk. . . . . . 11
Figure 2-8 Constructing the Payoff of Each node for Our Model. . . . . . . . . . 11
Figure 3-1 Determining the Stochastic Default Probability of Each Node. . . . . 13
Figure 3-2 Constructing the Payoff of Each Node Following a Stochastic Default
Probability. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
Figure 3-3 Determining the Constant Default Probability of Each Node. . . . . . 14
Figure 3-4 Constructing the Payoff of Each Node Following a Constant Default
Probability. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
Figure 3-5 Constructing the Payoff of Each Node without Default Probability. . 14
Figure 3-6 CB Value as a Function of ˙E. . . . . . . . . . . . . . . . . . . . . . 17
Figure 3-7 CB Value as a Function of Debt Ratio. . . . . . . . . . . . . . . . . . 18

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