Switching Asymmetric GARCH and Options on a Volatility Index

Few proposed types of derivative securities have attracted as much attention and interest as option contracts on volatility. Grunbichler and Longstaff (1996) is the only study that proposes a model to value options written on a volatility index. Their model, which is based on modeling volatility as a GARCH process, 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 model among GARCH, EGARCH, and GJR-GARCH demonstrates that a switching regime EGARCH model fits the data best. Next, the values of European call options written on a volatility index are computed using Monte Carlo integration. 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.