以動態模型計算遠期擔保債權憑證分券的選擇權價格

Abstract

相對於傳統的靜態Copula模型，本文提供一個動態模型來配適市場的信用違約交換價差，在此模型中，違約強度受到兩個因素影響，一個是漂移項，其會隨著時間遞增；另一個則是Impulse項，在本篇論文中，我們採用兩種型態的跳躍模型，分別是指數型態及線性型態的跳躍，這個Impulse就扮演著Gaussian Copula Function中違約相關性的角色。 我們並以此配適的參數，計算Forward CDO的分券價格。我們比較了Poisson搭配指數型跳躍或是線性跳躍所得到的計算結果，並觀察自2008年金融風暴發生之後，Forward CDO分券價格的走勢，分別從橫剖面及縱剖面來看，不同的到期年份及不同順位的分券，其價格的特性，以及隱含的資產相關性的變化。 基於Hull and White (2008) 的模型，我們接著計算以這些分券為標的物的選擇權價格，並根據Black形式的公式，推算每個分券的隱含波動性 (Implied Volatility)。

In this thesis, we present a dynamic model to calibrate the market quote of credit default swap spread, on the contrary to the traditional static Gaussian Copula model. In this dynamic model, the default intensity is affected by two factors: the first is the deterministic drift term, which increases over time; the other one is the Impulse term. We take two forms of impulse terms, which are exponential jump and linear jump. The jump size is a measure of default correlation as is the correlation matrix in the Gaussian Copula Function. We then calculate the prices of forward start CDO tranches. We compare the results of Poisson process with exponential jump and linear jump respectively, and observe the trend of price movement since the emergence of global financial crisis after mid 2008. Then we analyze the characteristics of forward start CDO tranches in terms of different maturity dates and different seniorities. Based on the Hull and White (2008) model, we calculate the prices of option on forward CDO tranches, and derive the implied volatility for each tranche based on the Black type formula.