Validation of volatility models

Abstract

In forecasting a financial 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 an ‘economic value’ since volatility is a tradable quantity (e.g. in options and other derivatives) in addition to being a risk measure. We analyse the fidelity 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.