Analysis of Financial Time Series, Third Edition

7.3 Econometric Approach to VaR Calculation

A general approach to VaR calculation is to use the time series econometric models of Chapters 2–4. For a log return series, the time series models of Chapter 2 can be used to model the mean equation, and the conditional heteroscedastic models of Chapter 3 or 4 are used to handle the volatility. For simplicity, we use GARCH models in our discussion and refer to the approach as an econometric approach to VaR calculation. Other volatility models, including the nonlinear ones in Chapter 4, can also be used.

Consider the log return rt of an asset. A general time series model for rt can be written as

7.5

7.6

Equations (7.5) and (7.6) are the mean and volatility equations for rt. These two equations can be used to obtain 1-step-ahead forecasts of the conditional mean and conditional variance of rt assuming that the parameters are known. Specifically, we have

If one further assumes that ϵt is Gaussian, then the conditional distribution of rt+1 given the information available at time t is . Quantiles of this conditional distribution can easily be ...