Neural networks are not very popular in finance and suffer from several problems:
The coefficient estimates from neural networks do not have any real theoretical interpretation
Virtually no diagnostic or specification tests are available for estimated models
They can provide excellent fits in-sample to a given set of ‘training’ data, but typically provide poor out-of-sample forecast accuracy
This usually arises from the tendency of neural networks to fit closely to sample-specific data features and ‘noise’, and so they cannot ‘generalise’
The non-linear estimation of neural network models can be cumbersome and computationally time-intensive, particularly, for example, if the model must be estimated repeatedly when rolling through a sample.
The simplest model for volatility is the historical estimate
Historical volatility simply involves calculating the variance (or standard deviation) of returns in the usual way over some historical period
This then becomes the volatility forecast for all future periods
Evidence suggests that the use of volatility predicted from more sophisticated time series models will lead to more accurate forecasts and option valuations
Historical volatility is still useful as a benchmark for comparing the forecasting ability of more complex time models