鞍點近似法於擔保債權憑證之評價與避險

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許書銘(Shu-Ming Hsu) 查詢紙本館藏

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財務金融學系

論文名稱

鞍點近似法於擔保債權憑證之評價與避險
(Saddlepoint Approximation for Pricing and Hedging Synthetic CDO)

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摘要(中)

本文在單因子高斯連繫結構模型下, 使用鞍點近似法求算損失函數,
以及計算擔保債權憑證分券的公平價差, 分券現值, 以及其對信用價差的敏感度, 及分券避險比例。
傳統上利用遞迴方法計算分券現值敏感度時,
假設信用價差變動 1 個基點, 求算其分券現值變化量, 但此法計算效率較低。
本文主要的貢獻在於利用鞍點近似法導求公平價差及分券現值敏感度之半解析公式解。

摘要(英)

This paper utilizes the saddlepoint approximation method to calculate loss distribution in the one factor Gaussian copula model, and evaluates the fair spread and mark-to-market of CDO tranches. Moreover, we analyze the sensitivity of the fair tranche spread to the changes of underlying portfolio spreads and work out the mark-to-market and hedge ratios for the tranches. Traditionally, using recursive method to calculate the sensitivity of mark-to-market has assumed a parallel shift of 1 basis point in the spread of the single name CDS or the underlying portfolio spreads. The recursive approach makes computation of mark-to-market and hedge ratios less efficient due to computing burden. Hence, the main contribution of this paper is to use saddlepoint approximation method to get semi-analytic formula for the sensitivity of fair spread and mark-to-market.

關鍵字(中)

★ 擔保債權憑證評價
★ 損失分配函數
★ 鞍點近似法
★ 因子聯繫模型
★ 擔保債權憑證避險

關鍵字(英)

★ Hedging CDO
★ Loss Distribution
★ Pricing CDO
★ Factor copula
★ Saddlepoint approximation

論文目次

Contents
1 Introduction 1
2 Literature Review 3
3 The Model Framework 6
3.1 One Factor Copula Model . . . . . . . . . . . . . 6
3.2 Saddlepoint Approximation (SA) . . . . . . . . . . 8
3.3 SA in Factor Copula Model . . . . . . . . . . . . 13
3.4 Pricing Synthetic CDO . . . . . . . . . . . . . . 15
3.5 Sensitivity of CDO . . . . . . . . . . . . . .. . 16
4 Numerical Result 19
4.1 Fair Spread of Each Tranche . . . . . . . . . . . 19
4.2 Sensitivity of Fair Spread . . . . . . . . . . . 22
4.3 Sensitivity of Mark-to-Market . . . . . . . . . . 23
4.4 Hedging Portfolio . . . . . . . . . . . . . . . . 25
5 Conclusion 30
Reference 32
A Gaussian integral 34
B Cauchy’s Theorem 35
C Saddlepoint Approximation 36
C.1 Saddlepoint Approximation of SA1 and SA2 . . . . 36
C.2 General Saddlepoint Approximation . . . . . . . . 37
D Saddlepoint Approximation of SA3 38
E Gaussian Hermite Integral 41

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指導教授

岳夢蘭(Meng-Lan Yueh)

審核日期

2008-6-26

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