條件獨立假設下合成型擔保債權憑證之評價與避險

The Pricing and Hedging of Synthetic CNOs Under the Conditional Independence Assumption

江彌修(Mi-Hsiu Chiang) ； 岳夢蘭(Meng-Lan Yueh) ； 林恩平(An-Ping Lin)

《財務金融學刊》 17卷1期 (2009/03) Pp. 1-40

https://doi.org/10.6545/JFS.2009.17(1).1

摘要

本文在違約事件為條件獨立（conditional independence）的假設了，利用Hull and White（2004）所提出之機率杓斗法則（probability bucketing method）建構結合成型擔保債權憑證債權群組（rclcrencepool）之損失分配，進而推導出用以計算分券信用價差的半解析式（semi-analytic）價差模型。本文利用半解析式評價模型求得分券信用價差，並提供風險因子負載係數（factor loadings）與回復率（re covery rate）之於各分券信用價差的敏感度分析。本文以實務界所採用的三種分券風險衡量指標來分析合成型擔保債權憑證各分券之相對風險特徵。術值結果顯現債權群組之已實現損失（realized loss）對於各分券的相對風險有不同程度的影響，已實現損失雖然對權益分券造成損害，卻同時降低了權益分券發生損失的不確定性。反觀次償分券，當已實現損失侵蝕其次順位信用保護層（subordination Ievel）後，次償分券發生損失的機率增加，相對風險因而提高。本文最後求算分券避險參數並提供避險分析。研究發現利用信用指數避險之避險成本高將使次償分券和先償分券在避險後的淨收入為負，此時分券投資人可考慮賣Delta值較高之單一資產信用違約交換，以規避特定信用標的之價差變動風險來達到某種程度的避險效果。

關鍵字

合成型擔保債權憑證 ； 因子連繫結構 ； 分卷避險比例 ； 損失分配

並列摘要

In this paper we investigate the valuation and hedging issues of synthetic collateral debt obligations (CDOs) under the conditional independence assumption. The probability bucketing method of Hull and White (2004 ) enables us to construct the loss distribution. and we characterize the correlation structure between defaults based on the factor-copula formalism initiated by Laurent and Gregory (2003 ) to arrive at a semi-analytic valuation framework. We consider risk measures that are adequate for assessing the relative risks of tranches. Efficient calculation of the hedging parameters is demonstrated, and we provide an in-depth analysis for the relevant hedging implications followed from our numerical results.

並列關鍵字

synthetic COOs ； factor copulae ； tranche Deltas ； loss distributions

參考文獻

Altman, E.I.,B. Brady,A. Resti,A. Sironi(2005).The link between default and recovery rate: theory, empirical evidence and implications.Journal of Business.78,2203-2228.

Andersen, L.,J. Sidenius,S. Basu(2003).All your hedges in one basket.Risk Magazine.November

working paper

Black, F.,J. C. Cox(1976).Valuing corporate securities: some effects of bond indenture provisions.Journal of Finance.31,351-367.

Bluhm, C.,L. Overbeck,C. Wagner(2002).An introduction to credit risk modeling.Chapman and Hall.