MODELING MARKET RISK USING EXTREME VALUE THEORY AND COPULAS Omari Cyprian Ondieki / A Research Proposal Submitted Inpart.ial fulfilment of the Requirements for the Degree of Doctor of Philosophy in Statistics of University of Nairobi 2013 Abstract Assessing the extreme events is crucial in financial risk management. All risk managers and financial institutions want to know the risk of their portfolio under rare events scenarios. This means there is not only a need to design proper risk modelling techniques which can predict the probability of risky events in normal market conditions but also a requirement for tools which can assess the probabilities of rare financial events; like the recent Global Financial Crisis (2007-2008). Extreme Value ;Theory (EVT) is an obvious '.l candidate, when dealing with extreme financial events and t~e quantification of extreme market risk. Extreme Value Theory provides well established statistical inodels for the computation of extreme risk measures llke the Return Level, ..Value at, Risk and Expected .. . .... ,; . .,~- '. ,. ,-. . - . , .... ,," . Shortfall. In this research we propose to describe the theoretical foundation of the extreme value theory and its potential in financial risk management. In relation to this, we will emphasize the statistical issues and limitations of the theory with applications in financial risk management in mind. Moreover, we will discuss how the theory may be applied to financial data and the specific issues that may arise in such applications. Also, we will introduce the issue of working with multivariate risk factors using copula theory and discuss some copula r results in multivariate extreme value theory. The research study will focus on an empirical study of the performance of EVT-based risk measurement methods based on five selected currency exchange rates: KSH/USD, KSH/GBP, KSH/EUR, KSH/ JPY and KSH/RAND. The p€,~formanceof the methods will be evaluated by their ability to accurately estimate well-known risk measures such as Value at Risk (VaR) and Expected Shortfall (ES). 1 Finally, we will compare the performance of EVT-based risk measurement methods for estimating risk measures. The performance of the model will be evaluated by its ability to accurately estimate well-known risk measures such as Value at Risk (VaR) and Expected Shortfall (ES). We will also backtest VaR and ES estimates at different confidence levels to validate the proposed model. Keywords: Extreme Value Theory, copula, Value at Risk, and Expected Shortfall. / 2