Copula模型於風險整合與運算之應用

Abstract

此論文討論copula模型在財務風險管理上的應用，並專注於風險值(VaR)的估計。風險值是在一定的信心水準下，某金融資產在未來特定時期內的最大損失。使用傳統方法，如透過雙維的相關係數來整合風險，一般會發生風險低估的現象。而copula模型因為可以被彈性使用，而逐漸受到廣泛的歡迎。在此論文，我們將介紹一些常被運用的copula模型，並統整它們的性質。此外，我們也會回顧一些有名的雙維相關係數，並介紹尾端相關性的概念。這些用來整合風險的工具將被用來估計VaR。我們會透過模擬來比較這兩種VaR整合方法。最後，我們也會透過模擬來分析VaR估計對錯用copula或邊際分佈的敏感度。

The thesis considers the application of copula models in financial risk management. Here we focus on the estimation of Value-at-risk (VaR), which is the threshold loss value such that the probability that the loss during a given time horizon exceeds the value is the targeted confidence level. Traditional approaches using bivariate association measures to model the relationship between risks tend to underestimate the aggregated risk. Copula has gained increasing popularity due to its flexibility. In this thesis, we will introduce some commonly used copulas and summarize their properties. Besides, we will review some well-known bivariate dependence measures and introduce the concept of tail dependence. These dependence modelling tools will then be used to estimate VaR. We conduct simulations to compare two different approaches to estimate the aggregated VaR. Finally, the sensitivity of VaR estimation by using incorrect copulas or marginal distributions will be examined via simulations.