Applying value at risk and expected shortfall to time-discrete financial time series model

Abstract

In this dissertation we shall apply risk management tools through the use of conditional heteroscedastic models. We shall first examine in detail the theoretical framework of conditional hetroscedastic models, in particular the ARCH and GARCH models. These models are able to capture heteroscedasticity and other stylised facts present in financial data and thus they are widely used to model financial market volatilities in risk management applications. We shall fit adequate ARCH/GARCH models to the error processes of the three datasets under study, namely, monthly share prices of Apple Inc. and GO plc., and monthly exchange rate EUR/USD. Next, we shall focus our attention on measuring market risk. Market risk, often faced by financial institutions, relates to the uncertainty attached to the value of a financial position. Various measures have been proposed in literature to measure market risk, amongst which, the value at risk (VaR) measure emerged as widely accepted and adopted internationally. However, value at risk, unlike other coherent risk measures, does not encourage portfolio diversification in general. This is one of the main reasons why alternative risk measures such as the expected shortfall (ES), that overcome the limitations encountered by VaR, have been developed. In this work, we shall examine the consistency conditions and show that VaR is not a coherent risk measure for general distributions. Consequently, we shall discuss the ES as an alternative coherent risk measures. Ultimately, we shall determine the VaR and ES for a single asset portfolio for the datasets under study for an underlying homoscedastic process and an underlying heteroscedastic process simultaneously, over a defined time horizon and specified confidence level.