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SYSTEMATIC UNDERPREDICTION OF VOLATILITY IN MAXIMUM LIKELIHOOD METHODS
 

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.

  

Source: Abu-Mostafa, Yaser S. - Department of Mechanical Engineering & Computer Science Department, California Institute of Technology
Magdon-Ismail, Malik - Department of Computer Science, Rensselaer Polytechnic Institute

 

Collections: Computer Technologies and Information Sciences