臺灣博碩士論文加值系統

本文以一個考慮跳躍的信用市場模型定價信用違約交換(credit default swaps)與信用違約交換選擇權(credit default swaptions)。本文提出一個跳躍擴散模型，將信用違約交換的價差當作主要變數來計算信用違約交換選擇權的價格，其中跳躍的部份是以標點過程(marked point processes)以及複合波式過程(compound Poisson processes)來描述。藉著對跳躍部份的特別設定我們能夠推導出解析的定價公式。我們也提出兩個數值的實例來顯示本模型的彈性：第一個是違約機率的計算，第二個是信用違約交換選擇權的隱含波動度曲線之重製。

This paper describes the pricing of credit default swaps (CDS) and credit default swaptions using market model with jumps. We propose a jump-diffusion credit market model that treats the CDS spread as the major variable to value a credit default swaption, in which the jumps are modeled by the marked point processes (MPPs) as well as the compound Poisson processes. Analytic pricing formula exists under some appropriate specification on the jump part of the CDS spread dynamics. We also make two numerical illustrations to show the flexibility of this model: The first one is the calculation of default probability and the second one is the reproducing of implied volatility curve for credit default swaptions.

Content
1. Introduction 1
2. Model Settings and Review of Credit Market Model 3
2.1 Notations: 3
2.2 Some Important Relationships: 4
2.3: A Brownian-motion-based Credit Market Model 5
3. An Extension to Jump-diffusion Process 5
3.1 Model Pre-settings: Jumps in Two Forward Rates 5
3.2 Modeling with the Marked Point Processes 7
3.3: Constructing jump processes from MPPs 9
3.4: Modeling with the Compound Poisson Processes 10
4. Pricing Credit Default Swaps and Swaptions 11
4.1 Credit Default Swaps 11
4.2: Pricing Credit Default Swaptions 13
5. Numerical Illustrations 18
5.1 Default Probability and Survival Curve 18
5.2 Implied Volatilities of Credit Default Swaptions 22
6. Conclusion 24
References 26
Appendix A – Change of measure with the inclusion of jumps 28
Appendix B – Derivation of the swaption price 29

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