Extreme movements of the major currencies traded in Australia

Following the event such as Global Financial Crisis (GFC) in 2008, financial institutions have suffered significant financial losses. Central banks have continuously bailed out financial distressed firms. However, such decisions from central banks cast doubt on the adequacy of current risk management strategy to reduce risk. Hence, the necessity of establishing robust risk evaluation techniques to manage losses during extreme events is critical. In particular, Value-at-Risk (VaR) has become an important measure of risk since the implementation of Basel II in 2008 and continues to become an important feature in Basel III. Even though the properties of VaR are well established, robust construction and forecast of VaR based on historical data remain unresolved. This is due to the difficulties in identifying the dynamics in asset's returns and it is extremely difficult to construct robust forecast without knowing the underlying process that governs the data. This paper proposes to estimate VaR by applying the extended version of the Hill's (1975) tail index estimator proposed in Berkes, et al. (2003). The extension incorporates potential time varying conditional variance and thus, provides a more robust method to estimate the tail index. The paper will provide a concise overview on various tail index estimators and their extensions, including Mikosch and Starica (2000), Berkes, et al. (2003), Iglesias and Linton (2009) and Hill (2010). It also contains a brief overview on some of the popular conditional variance models, including the Generalized Autoregressive Conditional Heteroskedasticity (GARCH) model of Bollerslev (1986) and its asymmetric extension by Glosten, Jagannathan and Runkle (1993). This paper will then forecast the VaR of exchange rate returns by estimating the tail index using daily exchange rate data on AUD with USD and GBP from January 1984 to December 2012. This approach is based on Iglesias and Linton (2009), Iglesias (2012) and Iglesias and Lagoa Varela (2012), which applied the tail index estimator proposed in Mikosch and Starica (2000) and Berkes, et al. (2003). The paper will also present a comparison of VaR between different conditional variance models suggested by Jorion (1996, 2007) to investigate the robustness of VaR estimates by tail index.