Time-Varying Mixture Multiplicative Error Models for Implied Volatility

Abstract:     
In this paper, we incorporate time-varying mixing probabilities into univariate and bivariate mixture multiplicative error models. Switching between the regimes is governed by an observable predetermined variable. The models are applicable to positive-valued time series, and are particularly well-suited for different financial volatility measures. The flexibility afforded by non-constant regime probabilities facilitates capturing the high persistence in financial volatility regimes, as well as time-varying volatility of volatility. We apply the new models to the implied volatilities of call and put options on the USD/EUR exchange rate, using the lagged daily exchange rate return as the regime indicator. In one-step-ahead forecasting, both mean squared errors and directional accuracy improve when allowing for time-varying mixing probabilities. Further improvements are brought about by employing a bivariate instead of a univariate model.

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