臺灣博碩士論文加值系統

本文提出了定價金融衍生工具的方法和技術，包括股票選擇權的定價，信用價差評估和資本結構套利。
本文的第一篇文章是主要是討論股票選擇權的定價，介紹了一種更有效的雙變數二元樹型圖方法來定價股票選擇權。提出利用遠期利率為即期利率期望值的概念，將遠期利率曲線隨時間所形成的面積取代股價擴散過程的漂移項，結合與利率二元樹的“強制性重合”和“固定機率”的方法，組成雙變數二元樹型圖。經由數值模擬的研究，證明利用的雙變數二元樹型圖的方法來計算的選擇權價格是有效且準確。
本文的第二篇文章是利用股票選擇權來評估公司的信用利差。個股選擇權是一個標的物為其股票價格的選擇權，而公司的權益又是以公司資產的標的物的選擇權。因此，公司的股票選擇權是一種複合選擇權，是選擇權中的選擇權。本文利用Geske的複合選擇權公式推導出一套結合股票選擇權為限制條件的非線性聯立方程;有效計算公司的信用利差與違約機率。
本文的第三篇文章採用Chen和Yeh（2006）提出的多期結構式信用風險模型，擴展了Geske-Johnson（1984）的複合選擇權模型，以評估多期債務結構下資本結構套利的表現。在本文中，我們使用假設內生違約門檻的多期Geske-Johnson信用風險模型來預測公司的違約情況。Geske-Johnson模型是完整解釋整個債務結構的模型，並且透過推定的違約門檻去評價公司的資產價值。本文還建立了交易策略，並針對2004年至2008年間，北美369家公司進行資本結構套利，並分析套利的績效表現。

This dissertation presents methodologies and techniques for pricing financial derivatives, including pricing stock option, evaluating credit spread, and conducting capital structure arbitrage.
The first article of this dissertation concerns pricing stock options by bivariate binomial Lattices. This article introduces a more efficient bivariate binomial lattice method to price stock options. The proposed approach simply replaces the drift term of the stock price process by the integration of the forward rate curve over the horizon of the option’s maturity in conjunction with “compulsory recombination” and “fixed probability” of binomial algorithm for the interest rate. The numerical simulation studies as well as the theoretical justification show that the option prices computed by the proposed lattice approach can effectively and accurately converge.
The second article of this dissertation is using equity options to assess the credit spreads of a company. An individual stock option is an option underlying its equity price and a company’s equity is an option underlying the assets of the company. Hence, an equity option of a company is a compound option, an option on a call option. Using Geske’s compound option formula to derive a set of nonlinear simultaneous equations combined with constraint on equity value; efficiently solve the credit spread and access probability of default.
The third article of this dissertation uses a multi-period structural model developed by Chen and Yeh (2006), which extends the Geske-Johnson (1984) compound option model to evaluate the performance of capital structure arbitrage under a multi-period debt structure. In this article, we predict the default situations of a firm using the multi-period Geske-Johnson model that assumes endogenous default barriers. The Geske-Johnson model is the only model that accounts for the entire debt structure and imputes the default barrier to the asset value of the firm. This article also establishes trading strategies and analyzes the arbitrage performance of 369 North American obligators from 2004 to 2008.

1. Introduction 1
1.1 Background 1
1.2. Literature Review 2
1.2.1 Literature Review of Bivariate Binomial Lattices 2
1.2.2 Literature Review of Equity Option for Valuating Credit Spread 3
1.2.3 Literature Review of Capital Structure Arbitrage 5
1.3 Motivation and Objectives 7
1.4 Contributions of the Dissertation 8
2. Pricing Stock Options by Bivariate Binomial Lattices 10
2.1 Introduction 10
2.2 Research method 12
2.2.1 The interest rate binomial lattice 12
2.2.2 Constructing the quadrinomial lattice 16
2.2.3 The convergence of price 23
2.3 Simulation 26
2.3.1 The interest rate binomial lattice model 26
2.3.2 Numerical example of quadrinomial lattice model 27
2.3.3 The efficiency of calculation 29
2.3.4 The LSM simulation 30
2.4 Conclusion 31
3. Using Equity Options to Assess the Credit Spreads of a Company 41
3.1 Introduction 41
3.2 Methods 45
3.2.1 Credit spread with stock price 46
3.2.2 Credit spread with stock option 47
3.3 Data 52
3.4 Results and analysis 54
3.4.1 Source 54
3.4.2 Credit spread calculation and analysis 56
3.4.3 Regression analysis 65
3.4.4 Ranking analysis 66
3.5 Conclusions and recommendations 68
4. Evaluation of Conducting Capital Structure Arbitrage Using the Multi-Period Extended Geske-Johnson Model 69
4.1 Introduction 69
4.2 Credit risk models 73
4.2.1 CreditGrades model 73
4.2.2 Extended Geske-Johnson model 75
4.2.3 CDS spread calculation 77
4.2.4 Implementation of capital structure arbitrage 77
4.3 Trading strategy 78
4.4 Data collection 80
4.5 Comparison of models 81
4.6 Two cases 83
4.7 Trading results 85
4.8 Conclusion 87
5. Conclusions 103
Bibliography 104
Appendix 109

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