Forecasting volatilities in option pricing: An application of Bayesian inference

This study investigates the problem of forecasting volatilities used in option pricing models for live cattle and live hog futures. The forecast problem is cast in the framework of Bayesian inference. Six types of individual forecast models are used--GARCH models, ARIMA models, systems of simultaneous equations, systems of seemingly unrelated regressions, a naive model, and an implied volatility model (i.e., the "inverse" Black option model). Volatility forecasts are made with those individual models under two scenarios involving (1) forecasting over three time-to-maturity periods (six months, four months, and two months) and (2) forecasting one month ahead. Composite forecasts are formed via four methods--Bayesian, adaptive, regression, and averaging. The performances of the forecasts are evaluated using error statistics and timing tests.It is found that GARCH models perform well in forecasting volatilities over long periods. The systems of simultaneous equations and the systems of seemingly unrelated regressions also do well and are similar in forecast values and performance evaluations. The forecasting ability of the ARIMA models is mixed, while the general performances of the naive model and the implied volatility model are poor. Model performances tend not to relate to the length of the period in forecasting.Forecast combinations can reduce forecast error and improve forecastability in most cases and for most combination methods. While the method of averaging provides consistently good performances, the method of regression does a good job in forecast combinations if adequate sample sizes are available. Combinations of additional forecasts do not necessarily generate smaller forecast errors and higher forecastability.U of I OnlyETDs are only available to UIUC Users without author permissio