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博碩士論文 etd-0802106-185343 詳細資訊
Title page for etd-0802106-185343
論文名稱
Title
應用違約機率時間序列模型對衍生商品定價
Derivative pricing based on time series models of default probabilities
系所名稱
Department
畢業學年期
Year, semester
語文別
Language
學位類別
Degree
頁數
Number of pages
43
研究生
Author
指導教授
Advisor
召集委員
Convenor
口試委員
Advisory Committee
口試日期
Date of Exam
2006-06-14
繳交日期
Date of Submission
2006-08-02
關鍵字
Keywords
衍生性商品定價、倒閉機率、信用風險、自我迴歸模型、結構式、對數勝算比、縮減式
reduced-form, structural form, log odds ratios, derivative pricing, default probabilities, autoregressive, credit risk
統計
Statistics
本論文已被瀏覽 5709 次,被下載 4266
The thesis/dissertation has been browsed 5709 times, has been downloaded 4266 times.
中文摘要
近年來,具有信用風險的衍生性商品的定價問題越來越受到重視。我們利用條件倒閉機率的對數勝算比的自我迴歸時間序列模型對衍生性商品做定價。我們對所提出的對數勝算比模型,推導兩種衍生性商品債券和選擇權的定價公式。研究中發現,在結構式與縮減式方法中的條件倒閉機率的對數勝算比,亦可配適適當的自我迴歸時序模型。文章最後利用統計模擬的方法來探討公式的準確性。
Abstract
In recent years, people pay much attention to
derivative pricing subject to credit risk. In this paper, we proposed an autoregressive time series model of log odds ratios to price derivatives. Examples of the proposed model are given via the structural and reduced form approaches. Pricing formulae of the proposed time series models are derived for bonds and options. Furthermore, simulation studies are performed to confirm the accuracy of derived formulae.
目次 Table of Contents
1 Introduction 1
2 Literature review 2
2.1 Structural model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2.2 Reduced-form model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
3 The proposed models 5
3.1 Time series models of log odds ratios . . . . . . . . . . . . . . . . . . . . . 5
3.2 Examples of log odds ratio models . . . . . . . . . . . . . . . . . . . . . . . 6
4 The pricing formulae 8
4.1 Bond pricing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
4.2 Option pricing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
5 Simulation results 13
6 Conclusions and future work 16
Appendix A 17
Appendix B 21
Appendix C 31
參考文獻 References
References
Artzner, Philippe and Delbean Freddy (1995), Default risk insurance and incomplete
markets, Mathematical Finance 5, 187-195.
Black, Fischer and Myron Scholes (1973), The pricing of options and corporate liabilities,
Journal of Political Economy 81, 81-98.
Black, Fischer and John C. Cox (1976), Valuing corporate securities: Some e®ects of bond
indenture provisions, Journal of Finance 31, 351-367.
Du±e, Darrell and Kenneth J, Singleton (1999), Modeling Term Structures of Defaultable
Bonds, Review of Financial Studies 12, 687-720.
Jarrow, Robert A. and Stuart M. Turnbull (1995), Pricing derivatives on ‾nancial secu-
rities subject to credit risk, Journal of Finance 50(1), 53-86.
Klein, P. (1996), Pricing Black-Scholes Options with Correlated Credit Risk, Journal of
Banking and Finance, 20, 1211-1229.
Merton, Robert C. (1974), On the pricing of debt: The risk structure of interest rates,
Journal of Finance 29, 449-470.
Reisz, Alexander and Claudia Perlich (2004), A market-based framework for bankruptcy
prediction Working Paper, Baruch College and New York University.
Sunklodas, J. (1984) On the rate of convergence in the central limit theorem for strongly
mixing random variables. Lithuanian math. J., 24, 182-190.
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