Volatility options: Hedging effectiveness, pricing, and model error

Abstract

Motivated by the growing literature on volatility options and their imminent introduction in major exchanges, this paper addresses two issues. JEL Classification: G11, G12, G13.

Model risk adjusted hedge ratios

“…For a review of model risk modelling, refer to Derman (1996), Green and Figlewski (1999), Branger and Schlag (2004), Cont (2006), and Psychoyios and Skiadopoulos (2006). and many others, where the variance or volatility of the price process is itself stochastic; and local volatility as in Dupire (1994), Derman and Kani (1994), and Rubinstein (1994) where arbitrage-free forward volatilities are "locked-in" by trading options today.…”

Mean-Reverting Logarithmic Modeling of VIX

“…Psychoyios and Skiadopoulos [22] and Wang and Daigler [27] conduct some comparative studies about the above two categories of VIX future and VIX option pricing models in the aspect of hedging effectiveness and pricing accuracy. Their research results suggest that simpler models of the second kind perform equally well with or even better than the more complicated consistent models, such as the fully-specified Lin and Chang [17] model.…”

“…where the first measure is defined by the following Esscher transform 22) and the second measure Q 2 is the same as Q. In order to calculate the two tail probabilities Π 1 and Π 2 , conditional characteristic functions of lnV IX T on filtration F t are first derived by…”

“…Psychoyios and Skiadopoulos [22] and Psychoyios [21] recommend that the mean-reverting logarithmic model (denoted as MRLR) serves better than the meanreverting square root models (denoted as MRSR) in both aspects of fitting VIX historical data under the objective measure and calibrating VIX options under martingale measure.…”

“…The logarithmic models proposed in Psychoyios and Skiadopoulos [22] and Psychoyios [21] assumes that logarithm of VIX follows a OU process as Vasicek [26] . By adding upward jumps that follow exponential distribution into the MRLR model to construct mean-reverting logarithmic jump model (denoted as MRLRJ), Psychoyios [21] successfully get an explicit pricing formula for VIX option expressed by characteristic function of log-VIX in the MRLRJ model.…”