Applying a copula to the estimation of value-at-risk

• Main Authors: Ang, Fang Ting, Shen, Angela Xiao'Ou, Khoo, Isabella Hui Ling
• Other Authors: Wu Yuan
• Format: Final Year Project
• Language: English
• Published: 2013
• Subjects: DRNTU::Business
• Online Access: http://hdl.handle.net/10356/51305
• Institution: Nanyang Technological University

Value-at-Risk (VaR) is a common tool employed in the estimation of market risk. Traditionally, VaR of a portfolio is estimated through an assumption of normally distributed portfolio returns. Yet, as we delve further into the estimation of VaR, we believe that returns are not always normally distributed, and there are lapses in this assumption resulting in the underestimation of VaR. Hence, recognizing the importance of the accurate estimation of market risk, this paper seeks to introduce the theory of copula into the estimation of VaR to present a case where the use of copula in the Monte Carlo simulations of VaR results in a better estimation of VaR compared to the traditional assumption of normal distributions. In view of this, we simulate a portfolio containing two market risk factors, the foreign exchange rates of USD against JPY and GBP against JPY, and in particular chose to describe their dependence structure using the Clayton copula. Through the generation of pseudo random numbers making use of MATLAB, back-testing results have shown that using a copula provides a more reliable estimation of the VaR.