楊朝成臺灣大學：財務金融學研究所劉任昌Liu, Jen-ChangJen-ChangLiu2007-11-282018-07-092007-11-282018-07-092005http://ntur.lib.ntu.edu.tw//handle/246246/60812在Jamshidian(1989)對利率選擇權評價研究中，作者闡述了遠期平賭測度的用處。本研究也將利用這個技巧，說明風險性債券的評價過程，並且將這個過程示範於兩個發表於Journal of Fixed Income期刊的模型。首先，本文證明Cathcart and El-Jahel(1998)的評價模型存在封閉公式解，這個結果取代了原來作者所使用的複雜數值方法。其次，本文說明Schmid and Zagst's (2000)模型中個四個微分方程式求解過程，可以使用三個微分方程式即可。上述的結果都是利用遠期平賭測度轉換技巧達成的。The usefulness of the forward martingale measure has been demonstrated by Jamshidian (1989) in deriving a pricing formula for default-free bond options. By making use of this technique, this paper offers a greatly simplified approach to the valuation of defaultable bonds by revisiting two pioneering hybrid models published in the Journal of Fixed Income. First, Cathcart and El-Jahel's (1998) original numerical inversion of Laplace transformations for pricing defaultable bonds is replaced with a closed-form formula derived through the use of the forward martingale measure. Second, Schmid and Zagst's (2000) original four ordinary differential equations for pricing defaultable bonds are replaced by three ordinary differential equations via the use of the forward martingale measure again.1 Evaluating Defaultable Bonds under the Forward Martingale Measure 1 1.1 Introduction 2 1.2 The Framework 3 1.2.1 Pricing Default-free Bonds under the Spot Measure 4 1.2.2 Expressing Credit Spreads under the Forward Measure 5 1.2.3 Affine Structure 6 1.3 An Application to Cathcart and El-Jahel (1998) 7 1.4 An Application to Schmid and Zagst (2000) 11 1.5 Conclusions 14 2 Pricing Vulnerable Options and Risky Debts under Different Seniority Status 26 2.1 Introduction 27 2.2 Assumptions and Review of Default Risk Models 28 2.2.1 Debts as the Only Liability 29 2.2.2 Call Options as the Only Liability 30 2.2.3 Two Types of Liabilities 31 2.3 Model Description 32 2.3.1 When Debts Are Senior to Options 32 2.3.2 When Options Are Senior to Debts 33 2.3.3 When Both Are Equally Ranking 33 2.3.4 A Unified Framework 34 2.4 Monte Carlo Simulations 36 2.4.1 Simulations Based on Klein and Inglis (2001) 37 2.4.2 Simulations Based on Klein (1996) 38 2.5 Interpretation of the Results 38 2.5.1 The Correlation Rho Always Imposes a Positive Effect on Option Values 39 2.5.2 The Correlation Rho Can Have both Positive and Negative Effects on Debt Values 40 2.5.3 The Mixed Effects from both Rho and the Priority Status 42 2.5.4 Results Based on Klein (1996) 42 2.6 Conclusions 43 3 Life Insurance Liability Valuation with Stochastic Interest Rates 51 3.1 Introduction 52 3.2 The Model 54 3.2.1 Models without Continuing Monitoring 57 3.2.2 Models with Continuing Monitoring 57 3.2.3 Equilibrium Condition 60 3.3 Numerical Examples 61 3.4 Conclusions 631231823 bytesapplication/pdfen-US破產風險脆弱選擇權結構模型債權順位遠期平賭測度seniority statusdefault riskforward martingale measurestructural modelvulnerable optionsthesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/60812/1/ntu-94-D87723002-1.pdf