Systematic Underprediction of Volatility in Maximum Likelihood Methods

In forecastinga nancial time series, the mean prediction can be validated by direct comparison with the value of the series. However, the volatility or variance can only be validated by indirect means such as the likelihood function. Systematic errors in volatility prediction have anèconomic value' since volatility is a tradable quantity (e.g., in options and other derivatives)in addition to being a risk measure. We analyze the delity of the likelihood function as a means of training (in sample) and validating (out of sample) a volatility model. We report several cases where the likelihood function leads to an erroneous model. We correct for this error by scaling the volatility prediction using a predetermined factor that depends on the number of data points.