Implied volatility measures the uncertainty of the underlying's price implied from the options prices.
Implied volatility is calculated using a 100-step binary tree for American style options, and a Black-Scholes model for European style options. Interest rates are calculated using the settlement prices from the day’s Eurodollar futures contracts, and dividends are based on historical payouts.
The 30-day volatility is the at-market volatility estimated for a maturity thirty calendar days forward of the current trading day. It is based on option prices from two consecutive expiration months. The first expiration month is that which has at least eight calendar days to run. The implied volatility is estimated for the eight options on the four closest to market strikes in each expiry. The implied volatilities are fit to a parabola as a function of the strike price for each expiry. The at-the-market implied volatility for an expiry is then taken to be the value of the fit parabola at the expected future price for the expiry. A linear interpolation (or extrapolation, as required) of the 30-day variance based on the squares of the at-market volatilities is performed. V30 is then the square root of the estimated variance. If there is no first expiration month with less than sixty calendar days to run, we do not calculate a V30.
Please Note
- One of the basic assumption of the Black-Scholes model is that future underlying's price has log-normal distribution (in other words, the price return has normal distribution). Two consequences of such an assumption are (1) the underlying's price is always positive (2) the volatility is measure in price return percentage.
- We have seen oil future prices turn negative. This violates the assumption of the Black-Scholes model and it became inappropriate for option pricing for such underlyings. Thus we switched to the Bachelier option pricing model for these negative capable products. The Bachelier model assumes normal distribution of the underlying price, thus allowing the price to go to zero or negative. Same as the Black-Scholes model, implied volatility in the Bachelier model still measures the uncertainty of the underlying price, but in dollar terms instead of percentage. E.g. In Black-Scholes model, we may speak of implied volatility being 1%, meaning the market expects the standard deviation (most probable range) of the underlying price is within 1% of its current price. Whereas in the Bachelier model, we may say the implied vol is $1, meaning the market expects the standard deviation of the underlying price is with +/- $1 of its current price.