Generating Volatility Forecasts from Value at Risk Estimates
利用对称分位数区间与标准差的比例关系，将条件自回归风险价值（CAViaR）模型的分位数预测转化为波动率预测，实证表明该方法在多个股票指数和个股上优于GARCH模型和移动平均法。
Statistical volatility models rely on the assumption that the shape of the conditional distribution is fixed over time and that it is only the volatility that varies. The recently proposed conditional autoregressive value at risk (CAViaR) models require no such assumption, and allow quantiles to be modeled directly in an autoregressive framework. Although useful for risk management, CAViaR models do not provide volatility forecasts. Such forecasts are needed for several other important applications, such as option pricing and portfolio management. It has been found that, for a variety of probability distributions, there is a surprising constancy of the ratio of the standard deviation to the interval between symmetric quantiles in the tails of the distribution, such as the 0.025 and 0.975 quantiles. This result has been used in decision and risk analysis to provide an approximation of the standard deviation in terms of quantile estimates provided by experts. Drawing on the same result, we construct financial volatility forecasts as simple functions of the interval between CAViaR forecasts of symmetric quantiles. Forecast comparison, using five stock indices and 20 individual stocks, shows that the method is able to outperform generalized autoregressive conditional heteroskedasticity (GARCH) models and moving average methods.