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

許書銘(Shu-Ming Hsu)

指導教授 ： 岳夢蘭

國立中央大學/管理學院/財務金融學系/碩士(2008年)

摘要

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。

關鍵字

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

並列摘要

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.

並列關鍵字

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

參考文獻

Andersen, L. and J. Sidenius (2005), “Extensions to the Gaussian copula: random recovery and random factor loadings”, Journal of Credit Risk, 1.

Annaert, J., J. Lamoot, C. G. J. Batista and G. Lanine (2007), “Don’t fall from the saddle: the importance of higher moments of credit loss distributions”, University

Daniels, H.E. (1954), “Saddlepoint approximations in statistics”, The Annals of Mathematical Statistics, 25(4), 631–650.

Daniels, H.E. (1980), “Exact saddlepoint approximations”, Biometrika, 67(1), 59–63.

Daniels, H.E. (1987), “Tail probability approximations”, International Statistical Review, 55(1), 37–48.