信用違約交換指數之權益證券的基礎相關係數計算

Abstract

在擔保債權憑證中，利用基礎期望損失和片段式二次函數插值法可以為非標準化的批次證券評價出合理的信用利差。但是，根據林崇曜(2008)的發現，利用合理的信用利差所倒推出的基礎相關係數在權益證券中具有微笑的現象，產生雙重解的窘境。 本篇論文針對以上的缺點進行改善，試圖在權益證券中架構出一條單調遞增的基礎相關係數曲線，避免產生雙重解的窘境，方便實務上進行非標準化批次證券的定價。 未來可以針對不同型態的違約損失分配，例如：t分配、雙重t分配、伽馬分配…等，或是其他不同Copula的函數去比較不同模型的合理信用利差，找出最適合市場的信用風險模型和信用利差。

While pricing Collateral Debt Obligations, using base expected loss and piecewise quadratic interpolation can find the fair spreads for bespoke tranches without arbitrage. But, according to the master thesis of Mr. Lin Chung-Yao in 2008, the base correlation implied from the fair spreads calculated by base expected loss and piecewise quadratic interpolation would be smiling in the equity tranche. In order to improve the above-mentioned drawback, constructing a non-decreasing base correlation curve in the equity tranche would be the solution. My master thesis wants to construct a non-decreasing base correlation curve in the equity tranche by adding some constraints to the piecewise quadratic interpolation to avoid the smiling effect of the base correlation. In the future, comparing different spreads calculated from the different Copula models or different loss distributions would be an extensive research to find the fittest credit model to the market conditions.