Quantile forecasts of daily exchange rate returns from forecasts of realized volatility

Abstract

Quantile forecasts are central to risk management decisions because of the widespread
\nuse of Value-at-Risk. A quantile forecast is the product of two factors: the model used to
\nforecast volatility, and the method of computing quantiles from the volatility forecasts. In
\nthis paper we calculate and evaluate quantile forecasts of the daily exchange rate returns
\nof five currencies. The forecasting models that have been used in recent analyses of the
\npredictability of daily realized volatility permit a comparison of the predictive power of
\ndifferent measures of intraday variation and intraday returns in forecasting exchange rate
\nvariability. The methods of computing quantile forecasts include making distributional
\nassumptions for future daily returns as well as using the empirical distribution of predicted
\nstandardized returns with both rolling and recursive samples. Our main findings are that the
\nHeterogenous Autoregressive model provides more accurate volatility and quantile forecasts
\nfor currencies which experience shifts in volatility, such as the Canadian dollar, and that
\nthe use of the empirical distribution to calculate quantiles can improve forecasts when there
\nare shifts.