How do unexpected values affect GARCH models?

Unexpected values play a crucial role in GARCH (Generalized Autoregressive Conditional Heteroskedasticity) models because they directly impact the variance estimations of a financial time series. GARCH models are designed to model and predict the volatility of asset returns, which can vary over time and are influenced by past returns and the past conditional variances.

When unexpected values, or shocks, occur in the data, they induce changes in the forecasted volatility. These shocks contribute to the new conditional variance estimations, as GARCH models are built to adjust the forecasted variance based on the magnitude and frequency of these unexpected values. If larger-than-expected or unexpected returns are observed, the model will recalibrate the forecast of future volatility to account for this increased uncertainty.

Thus, the correct answer underscores the fundamental principle of GARCH models: the response of volatility to these unexpected shocks is central to their functionality and accuracy in estimating future variance. This is particularly important for risk management and derivative pricing, where understanding and predicting volatility is essential.