Sensitivity analysis of credit derivatives

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曾耀德(Yao-Te Tseng) 查詢紙本館藏

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論文名稱

(Sensitivity analysis of credit derivatives)

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摘要(中)

信用型衍生性商品 (Credit derivatives) 為重要的風險管控的重要工具
,可做為投資者轉移性用風險的重要商品,當要對信用型衍生性商品作分析預測與風險管理時如何計算信用型衍生性商品的敏感度成為重要的議題。本文特別應用了distribution theory 對信用型衍生性商品的價格敏感係數 (Greeks) 提供的一個不偏的估計量,文中對 the likelihood ratio method以及我們的新方法在計算 deltas、gammas、以及 cross-gammas 的效率做了比較,數值模擬驗證了我們的方法提供的估計是比較有效率的。

摘要(英)

Credit derivatives have been hugely popular, as they provide a nice mechanism to transfer credit risk for investors. Sensitivity analysis for credit derivatives is essential for both
speculation and hedging purposes. This paper considers the Greeks calculation for credit
derivatives. In particular, we provide a direct method via the distribution theory that gives
unbiased estimators of the Greeks. We compare the efficiency of our proposed direct method
and the likelihood ratio method regarding deltas, gammas, and cross-gammas. Numerical
simulation confirms that our method yields more efficient estimators.

關鍵字(中)

★ 價格敏感係數
★ 信用型衍生性商品

關鍵字(英)

★ price sensitivity
★ Greeks
★ credit derivatives
★ Dirac delta function
★ simulation

論文目次

摘要 i
Abstract ii
誌謝 iii
List of Figures vi
Chapter 1 Introduction 1
Chapter 2 Our method 5
2.1 The Dirac delta method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2 Illustrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2.1 A typical way to calculate Greeks . . . . . . . . . . . . . . . . . . . . 11
2.2.2 The Dirac delta method . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.2.3 The likelihood ratio method . . . . . . . . . . . . . . . . . . . . . . . 12
2.2.4 Theoretical justifications . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.3 Simulation studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
Chapter 3 Applications 18
3.1 Introduction to Basket default swaps . . . . . . . . . . . . . . . . . . . . . . 18
3.2 Formulas of Greeks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.3 Simulation studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
Chapter 4 Conclusion 26
Appendix 30
A.1 Proof of Theorem 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
A.2 Proof of Proposition 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
A.3 Closed-form formulas of ∆LRM and ΓLRM
for hypothetical swaps . . . . . . . 33
A.4 Proof of Theorem 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
A.5 Proof of Theorem 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
A.6 Formulas of the delta for basket default swaps . . . . . . . . . . . . . . . . . 37
A.7 Formulas of the gamma for basket default swaps . . . . . . . . . . . . . . . . 40
A.8 Formulas of the cross gamma for basket default swaps . . . . . . . . . . . . . 46

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指導教授

鄧惠文(Huei-Wen Teng)

審核日期

2014-7-7

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