Application of extreme value theory for estimating daily brent crude oil prices

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Assessing the probability of rare and extreme events is an important issue in the risk management of financial portfolios. Crude oil markets are highly volatile and risky. Extreme Value Theory (EVT), an approach to modelling and estimating risks under rare events, has seen a more prominent role in risk management in recent years. This thesis presents an application of EVT to the daily returns of Brent crude oil prices in the spot market between 1987 and 2009. We focus on the peak over threshold method by analysing the generalized Pareto distributed exceedances over some high threshold. This method provides an effective means for estimating tail risk measures specifically, Value-at-Risk (VaR) and Expected Shortfall (ES). The estimates of these risk measures computed under high quantile (99th percentile) provides estimates of VaR as 8.1% and 8.0% for daily positive and negative returns, respectively. The estimates for expected shortfall are 12.3% and 10.7% for daily positive and negative returns, respectively.
A thesis submitted to the Department of Mathematics, Kwame Nkrumah University of Science and Technology in partial fulfilment of the requirements for the degree of Master of Science.