VIX Option Pricing and CBOE VIX Term Structure : A New Methodology for Volatility Derivatives Valuation

The study proposes an arbitrage-free methodology of VIX term structure modeling that is tailored to handle the most actively traded VIX options. Under the model, the evolution of future VIX is completely determined by the volatility function of forward VIX squared normalized by VIX futures prices. A general volatility function with one- to three-factor models is used to examine their pricing for VIX options across strikes and maturities from February 24, 2006 to September 30, 2008. The primary contributions of this article are (i) taking as given CBOE VIX Term Structure to specify a general stochastic structure upon forward VIX, (ii) proposing an arbitrage-free closed-form solution to the VIX option value with the general volatility function that incorporates mean-reversion and hump effects to test two multifactor models, (iii) finding that the class of multifactor models outperforms the classes of one- and two-factor models, and (iv) finding that models with hump volatility function perform better than other models. Pricing with three-factor models gives the benefit of eliminating most moneyness and maturity biases, especially for ATM and OTM options. Correctly specified and calibrated, the single-factor Hump model may be superior to inappropriate multi-factor Exponential models in pricing