There are different methods for extracting probabilities from options prices. A number of these involve estimating a probability density function (PDF) by inverting an options pricing formula such as Black-Scholes and using option market prices to solve for the pricing density function. Most theoretical option pricing models rely on an assumption of lognormally distributed prices, or normally distributed log returns. These models assume this standard normal density function applies to value an option of any strike price for a given expiration. Observed futures price returns, however, may not conform to a standard normal distribution. Observed returns may be skewed or kurtotic, meaning the realized price distributions could have greater probabilities of extreme price moves and tend to cluster more returns around current futures price levels versus these models. The effect on option prices in the market is for volatility to vary by strike price. Instead of the same volatility for each option strike, “implied volatilities” will differ by strike. These strike and time-varying implied volatilities imply a probability density function of futures returns that may have greater skew or kurtosis than a standard normal.

It is possible to estimate this non-standard normal probability density function by inverting theoretical value equations and solving for an implied probability distribution that fits current option market prices. Note, different methods can yield slightly different implied probabilities as more than one density function can satisfy current option prices, given the same constraints. The method used for the CME OPEC Watch Tool probabilities is as follows:

D N (d2)/D Moneyness

Where Moneyness is defined as Log(K/F)/Sqr(dte)

1. Implied volatilities are calculated and fitted by a fitting function (of the form x^n) from current option and futures prices on the LOQ5 contract and from the nearest active Crude Oil Weekly option prices. An implied volatility curve for a generated July 6 expiration is interpolated from these available option expirations.
2. From the implied volatility function, the value N (d2) is calculated by strike (k), where N (d2) is defined as:

3. The ATM (at-the-money) implied volatility from the generated July 6 expiration is priced, and a 1-standard deviation range is calculated from that implied volatility and time to expiration.
4. The 1-standard deviation range is recalibrated at 14, 7 and 4 days to expiration (DTE).
5. The 1-standard deviation range is applied to the centering reference future price.
6. The implied event probabilities are then set as:
   • The probability area ≥ +1 SD price will be the ‘Small Increase’ %
   • The probability area ≤ -1 SD price will be the ‘Larger Increase’ %
   • The probability area > -1 SD and < +1 SD will be the ‘Expected Increase’ %