Scaling Conditional Tail Probability And Quantile Estimators

A key issue for risk management in practice is to decide the relevant horizon associated with risk measurement. Many different horizons may be relevant from short (e.g. daily) to long (e.g. monthly) timeframes and the risk manager must be able to provide measures across a range of horizons. This paper measures risk at different horizons using volatility forecasts at high frequency as inputs that are then scaled for longer horizons. In terms of risk measurement probability and quantile risk estimation has developed enormously in the past decade from Value at Risk (VaR) measures to coherent measures such as Expected Shortfall.