Stochastic volatility forecasting and risk management

Abstract

This paper compares the forecasting performance of the range-based stochastic volatility model with a number of other well-known forecasting models. Each forecasting model is applied to a financial data set that includes daily futures prices on, the S&P 500, ten year US government bond series, crude oil prices, and the foreign currency exchange rate between the Canadian and US dollar. Forecasts are evaluated out of sample using forecast summary statistics as well as value at risk measures like conditional coverage, independence and unconditional coverage. Overall the forecast summary statistics show that for each financial series, moving average, exponential smoothing and AR5 models to be better at forecasting the log range than the stochastic volatility model. Value at risk calculated from the stochastic volatility models does not reject independence in each of the four financial series studied but does reject conditional and unconditional coverage in all of the series studied. The empirical density model does not reject unconditional coverage in three out of the four financial series studied. All of the parametric models reject conditional coverage. These results show how difficult it is to design a good parametric value at risk model.

Acknowledgements

Parts of this paper were presented at the 11th Annual Global Finance Conference in Las Vegas. I thank participants for their useful comments.

Notes

The reported results for forecast summary statistics, value at risk, and their respective rankings are reasonably robust for small (one or two year) changes in the estimation sample size.

In the analysis that follows, probability values from the DM and RT tests are being compared to 0.05.