Valuation of options on the VIX – a heuristic approach

In this paper, we present a simple parameterisation of the volatility surface in options whose underlying is the implied volatility from options on the S&P 500 as expressed by the VIX index. In particular, we show that: (i) the implied volatility of ATM options on the VIX is highly correlated with the volatility smile of options on the S&P 500; (ii) the ATM implied volatility of options on the VIX decreases exponentially with option expiry; (iii) the volatility smile of options on the VIX can be well described by the popular stochastic volatility model SABR. Using the simple rules of thumb described in paras. (i)-(iii), it is possible to give the price (implied volatility) of an option on the VIX with any term and strike price, obtaining a value close to the market.