Estimating Financial Risk Measures for Futures Positions:A Non-Parametric Approach

This paper presents non-parametric estimates of spectral risk measures applied to long and short positions in 5 prominent equity futures contracts. It also compares these to estimates of two popular alternative measures, the Value-at-Risk (VaR) and Expected Shortfall (ES). The spectral risk measures are conditioned on the coefficient of absolute risk aversion, and the latter two are conditioned on the confidence level. Our findings indicate that all risk measures increase dramatically and their estimators deteriorate in precision when their respective conditioning parameter increases. Results also suggest that estimates of spectral risk measures and their precision levels are of comparable orders of magnitude as those of more conventional risk measures. Running head: financial risk measures for futures positions.

Fiscal fan charts - A tool for assessing member states’ (likely?) compliance with EU fiscal rules

This paper sets out a methodology for constructing fan charts for the government deficit and debt ratios over the medium-term. It relies on information contained in Stability/Convergence Programme Updates, a model of the relevant stochastic process (for example, the real GDP process) or processes, and a parameter estimate of the sensitivity of the primary budget balance to the output gap for the member state under consideration. A model of the dynamic deficit-debt relationship allows the impact of random output growth to work its way through the fiscal arithmetic in a consistent and traceable way to produce fan charts over a five-year forecast horizon. The initial set of fiscal fan charts included here for Ireland use the indicative public finance projections set out in the 2011 Update for Ireland. The range of possible fiscal outcomes in the charts assumes no fiscal policy response to any change in the budgetary position over the period such as could arise from changes in growth rates. This assumption of “no policy change” is a standard one in the construction of fan charts. Governments will, however, generally be in a position to adjust fiscal policy towards meeting a specific fiscal target, such as reaching a deficit position of less than 3 percent of GDP in the medium-term. A second set of fan charts is included which indicates how the probabilistic range of fiscal outcomes could be affected by a tightening of fiscal policy in 2013-2015.Programme Updates, fan charts, fiscal arithmetic, stochastic processes, prediction regions

Evaluating the Precision of Estimators of Quantile-Based Risk Measures

This paper examines the intra-day seasonality of transacted limit and market orders in the DEM/USD foreign exchange market. Empirical analysis of completed transactions data based on the Dealing 2000-2 electronic inter-dealer broking system indicates significant evidence of intraday seasonality in returns and return volatilities under usual market conditions. Moreover, analysis of realised tail outcomes supports seasonality for extraordinary market conditions across the trading day.Value at Risk, Expected Shortfall, Spectral Risk Measures, Moments, Precision.

Exponential Spectral Risk Measures

Spectral risk measures are attractive risk measures as they allow the user to obtain risk measures that reflect their subjective risk-aversion. This paper examines spectral risk measures based on an exponential utility function, and finds that these risk measures have nice intuitive properties. It also discusses how they can be estimated using numerical quadrature methods, and how confidence intervals for them can be estimated using a parametric bootstrap. Illustrative results suggest that estimated exponential spectral risk measures obtained using such methods are quite precise in the presence of normally distributed losses.

Intra-Day Seasonality in Foreign Market Transactions

Spectral risk measures are attractive risk measures as they allow the user to obtain risk measures that reflect their subjective risk-aversion. This paper examines spectral risk measures based on an exponential utility function, and finds that these risk measures have nice intuitive properties. It also discusses how they can be estimated using numerical quadrature methods, and how confidence intervals for them can be estimated using a parametric bootstrap. Illustrative results suggest that estimated exponential spectral risk measures obtained using such methods are quite precise in the presence of normally distributed losses.limit orders, market orders, tail risks