 
Summary: SYSTEMATIC UNDERPREDICTION OF VOLATILITY IN
MAXIMUM LIKELIHOOD METHODS
M. MAGDONISMAIL, Y.S. ABUMOSTAFA
Caltech 13693, Pasadena,
CA 91125, USA
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 analyze 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.
Keywords: Validation, Volatility Prediction, Maximum Likelihood
1 Introduction
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Figure 1.
