Modeling and forecasting implied volatility

This dissertation contains four essays, all of which model time series of implied volatility (IV) and assess the forecast performance of the models. The overall finding is that implied volatility is indeed forecastable, and its modeling can benefit from a new class of time series models, so-called multiplicative error models. It is often beneficial to model IV with two (or more) regimes to allow for periods of relative stability and periods of higher volatility in markets. The first essay uses a traditional ARIMA model to model the VIX index. As the data displays conditional heteroskedasticity, forecast performance improves when the model is augmented with GARCH errors. The direction of change in the VIX is predicted correctly on over 58 percent of trading days in an out-of-sample period of five years. An option trading simulation with S&P 500 index options provides further evidence that an ARIMA-GARCH model works well in forecasting changes in the VIX. The second essay estimates two-regime multiplicative error models for the implied volatility of options on the Nikkei 225 index. Diagnostics show that the model is a good fit to the data. The implied volatility of call options turns out to be more forecastable than the implied volatility of put options in a two-year out-of-sample period. A two-regime model forecasts better than a one-regime model. When the forecasts of the multiplicative models are used to trade options on the Nikkei 225 index, the value of using two regimes is again confirmed. The third essay investigates the joint modeling of call and put implied volatilities with a two-regime bivariate multiplicative error model. The data set is the same as in the second essay. Forecast performance improves when call IV is used as an explanatory variable for put IV, and vice versa. Forecasts with the bivariate model outperform forecasts obtained with the univariate models in the second essay. An impulse response analysis shows that put IV recovers faster from shocks, and the effect of shocks lasts for up to six weeks. The fourth essay models the IV of options on the USD/EUR exchange rate. This essay extends the models of the second and third essays with a time-varying probability between regimes. The changes in the USD/EUR exchange rate are used as a regime indicator, with large changes in the exchange rate signifying a more volatile regime. Out-of-sample forecasts indicate that it is beneficial to jointly model the implied volatilities derived from call and put options: both mean squared errors and directional accuracy improve when employing a bivariate rather than a univariate mode