Chapter 7Volatility Modeling

Perhaps the two most basic problems of risk management are the estimation of single-asset return volatilities and covariance matrices for the returns of asset portfolios. However, it is well known that maximum-likelihood estimates and other estimates widely used by practitioners are subject to nontrivial estimation error and lack responsiveness to changing market conditions, and as a result their forecasting performance is generally unsatisfactory.

With volatility modeling, as with other aspects of our modeling enterprise, our goals are twofold. First, we seek methods that will furnish maximally responsive online estimates for changing market conditions. All estimates should be computable based on information available at the present date, without creating undue prejudice concerning their reliability in forecasting. Second, we seek to expose degrees of freedom where alternative decisions can be made concerning the form of the model. Volatility is not simply ‘out there’ to be found for every asset, and, depending on a variety of other modeling choices, the form and value given to volatility can vary significantly. We shall see this again in Chapter 8 when the volatility of oil futures prices is decomposed into spot price volatility, convenience yield volatility, and interest rate volatility.

Reexamining the fundamentals of volatility and covariance matrix estimation with Bayesian methods thus entails comparing the forecasting performance of online ...

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