Scaling conditional tail probability and quantile estimators

We present a novel procedure for scaling relatively high frequency tail probability and quantile estimates for the conditional distribution of returns.

Varying the VaR for Unconditional and Conditional Environments,

Accurate forecasting of risk is the key to successful risk management techniques. Using the largest stock index futures from twelve European bourses, this paper presents VaR measures based on their unconditional and conditional distributions for single and multi-period settings. These measures underpinned by extreme value theory are statistically robust explicitly allowing for fat-tailed densities. Conditional tail estimates are obtained by adjusting the unconditional extreme value procedure with GARCH filtered returns. The conditional modelling results in iid returns allowing for the use of a simple and efficient multi-period extreme value scaling law. The paper examines the properties of these distinct conditional and unconditional trading models. The paper finds that the biases inherent in unconditional single and multi-period estimates assuming normality extend to the conditional setting.

Modelling extreme financial returns of global equity markets

Extreme asset price movements appear to be more pronounced recently and have major consequences for an economy’s financial stability and monetary policies. This paper investigates the extreme behaviour of equity market returns and quantifies the probabilities of these losses. Taking fourteen major equity markets the study is able to ascertain similarities and divergences in the tail returns from around the world. To do so, it applies extreme value theory to equity indices representing American, Asian and European markets. The paper finds that all markets tail realisations are adequately modelled with the fat-tailed Fréchet distribution. Furthermore tail realisations associated with the downside of a distribution are greater than those associated with the upside, and extreme returns for Asian markets are usually larger than their European and American counterparts.

Volatility and the Euro: an Irish perspective

With Ireland joining the Euro, exchange rate risk between participating states is gone. However, as is known, this new currency will continue to face exchange rate risk, and the general reduction of volatility on a day to day basis for Irish economic agents neglects to take account of possible extreme problems with the Euro. In this paper we will see that even though the Euro is a managed (irrevocably fixed) system, trade between Ireland and non-members, most notably the US, involves two separate currencies. This trade will require currency trading, leading to the possibility of large downside exposure to exchange rate risk for Irish exporters. In order to determine the extent to which the currencies can fluctuate, this paper examines exchange rate volatility using an Extreme Value approach. A number of different volatility scenarios are offered based on extrapolation of different exchange rate regimes under two broad headings, floating and managed. Using these headings, a number of actual systems are analysed including the ERM, the Snake in the Tunnel and Bretton Woods.

Tail Behaviour of the Euro

This paper empirically analyses risk in the Euro relative to other currencies. Comparisons are made between a sub period encompassing the final transitional stage to full monetary union with a sub period prior to this. Stability in the face of speculative attack is examined using Extreme Value Theory to obtain estimates of tail exchange rate changes. The findings are encouraging. The Euro’s common risk measures do not deviate substantially from other currencies. Also, the Euro is stable in the face of speculative pressure. For example, the findings consistently show the Euro being less risky than the Yen, and having similar inherent risk to the Deutsche Mark, the currency that it is essentially replacing.