Tail Risk Modelling

Nigel Da Costa Lewis

The occurrence of rare, yet extreme, events seem to becoming more apparent in financial markets around the globe. The financial crisis of 2008, the slump in global economic activity and the banking crisis in Europe and the US mean there is greater need to design robust risk modelling techniques which can predict the probability of rare risky events. VaR models have dominated to landscape for capturing large-scale portfolio risk. We will explore some of these models in this chapter. Extreme value theory (EVT) provides well-established statistical models for the computation of extreme risk measures such as the return level, value-at-risk and expected shortfall. In this chapter, we will also detail the statistical modelling of extreme observations using EVT. We begin first with an overview of VaR modelling.

VALUE-AT-RISK MODELLING

The potential for significant losses in a firm’s portfolio of assets is a major concern of portfolio managers, investors and regulators. VaR addresses this concern directly by providing a probabilistic measure of extreme market risk. The output is a single number representing the risk inherent in a portfolio. It therefore reduces the complexities of risk