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.

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

Spectral Risk Measures with an Application to Futures Clearinghouse Variation Margin Requirements

This paper applies an AR(1)-GARCH (1, 1) process to detail the conditional distributions of the return distributions for the S&P500, FT100, DAX, Hang Seng, and Nikkei225 futures contracts. It then uses the conditional distribution for these contracts to estimate spectral risk measures, which are coherent risk measures that reflect a user’s risk-aversion function. It compares these to more familiar VaR and Expected Shortfall (ES) measures of risk, and also compares the precision and discusses the relative usefulness of each of these risk measures in setting variation margins that incorporate time-varying market conditions. The goodness of fit of the model is confirmed by a variety of backtests.