Pricing VIX derivatives under Double-Mean-Reverting Logarithmic Model

There have been numerous attempts to derive the fair price of VIX derivatives under various stochastic models. And D. Psychoyios shows the fact that the mean-reverting logarithmic diffusion with jumps well approximate the... [ view full abstract ]

There have been numerous attempts to derive the fair price of VIX derivatives under various stochastic models. And D. Psychoyios shows the fact that the mean-reverting logarithmic diffusion with jumps well approximate the market of the volatility index in his work, 2010. This paper extend this mean-reverting logarithmic model as double-mean-reverting process to obtain improved consequences for VIX derivatives pricing. We derive characteristic functions of our given models and exploit these characteristic functions to obtain the price of VIX derivatives. Through numerical experiment, we perform calibration to market data and examine sensitivity of parameters by providing greeks under our models.