Garch Models: Forecasting Volatility and Pricing Options - Joshi, Sahil (2010)
Volatility is unobservable and a very essential input to the option pricing models and for risk management purposes. Historical volatility is not a good indicator of future volatility and in the literature GARCH model of Bollerslev (1986) is often proved to be very accurate in forecasting future volatility which also led to the extension of other GARCH models overcoming its limitations. In this paper, accuracy of three popular GARCH models, GARCH(1,1), GJR-GARCH(1,1) & EGARCH(1,1) is compared with the actual realized volatility in case of $/£ exchange rate. The pricing performance of alternative GARCH models in pricing currency options is paid very little attention in literature. Therefore, in this paper the pricing performance of GARCH option pricing model with three alternative GARCH models and widely used Garman-Kohlhagen model is also compared with the market settled GBP European currency option prices. In case of forecasting volatility, even though the GJR-GARCH(1,1) and EGARCH(1,1) model incorporates the asymmetric effect, the GARCH(1,1) model is proved to be superior than other two models even after having few limitations. Regarding the option pricing, GARCH option pricing model with GARCH(1,1) volatility is overall better than the other models.