Switching Asymmetric GARCH and Options on a Volatility Index
Journal of Futures Markets, Vol. 24, pp. 251-282, March 2004
Posted: 8 Feb 2004
Few proposed types of derivative securities have attracted as much attention as option contracts on volatility. Grunbichler and Longstaff (1996) proposes a model to value options written on a volatility index. Their model does not take into account the switching regime and asymmetry properties of volatility. We show that the Grunbichler and Longstaff (1996) model underprice a 3-month option by about 10%. A Switching Regime Asymmetric GARCH is used to model the generating process of security returns. The comparison between the switching regime model and the traditional uni-regime GARCH used by Grunbichler and Longstaff (1996) demonstrates that the switching regime EGARCH model fits the data best. When comparing the values of the option based on the Switching Regime Asymmetric GARCH model and the traditional GARCH specification, it is found that the option values obtained from the different processes are very different. This clearly shows that the Grunbichler-Longstaff model is too stylized to be used in pricing derivatives on a volatility index.
Keywords: Option pricing, volatility index, switching regime, GARCH
JEL Classification: G13, C22
Suggested Citation: Suggested Citation