Switching asymmetric GARCH and options on a volatility index

Abstract

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 underprices a three-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

Volatility options: Hedging effectiveness, pricing, and model error

“…Hence, the previously reported results are robust to the choice of a zero value for the volatility risk premium. This is in line with the results in Daouk and Guo (2004) who also found that the effect of model error on the pricing performance of the GL model is not affected by the choice of the volatility risk premium.…”

“…For example, Brenner et al (2001) suggest the introduction of options on straddles. Finally, it may be worth studying the hedging effectiveness of volatility options and the impact of model error for alternative data generating processes (see e.g., Wu 2002, andDaouk andGuo 2004). In the interests of brevity, these extensions are best left for future research.…”

“…This may be surprising given that one of the main arguments for introducing volatility options is based on their use as hedging instruments 1 . Furthermore, the comparative hedging and pricing performance of the existing volatility option pricing models in the presence of model error has attracted very little attention 2 ; Daouk and Guo (2004) have focused on the pricing side and they have investigated the impact of model error to the performance of only one (Grünbichler and Longstaff 1996) of the developed volatility option pricing models.…”

“…MC simulation has been used in the literature extensively to investigate the pricing and hedging performance of various models, as well as the impact of model error (see e.g., Hull and White 1987, Figlewski 1989, Jiang and Oomen 2001, Carr and Wu 2002, Daouk and Guo 2004. This is because it enables the selection of the data generating process, and the control of the values of its parameters.…”

A Jump Diffusion Model for VIX Volatility Options and Futures

“…These were based on a discrete-time GARCH volatility process and its continuous time counterpart developed by Heston and Nandi (2000b). Recently, Daouk and Guo (2004), studied the valuation of volatility options based on a Switching Regime Asymmetric GARCH process for the underlying.…”