Options pricing models include two that are online as free Excel worksheet programs at www.futuresmag.com: The Black-Scholes model and LLP (log-log parabola) model.
Black-Scholes and similar models were critical to the development of trading at facilities such as the Chicago Board Options Exchange (CBOE) in 1973. As theoretical pricing programs that may be computerized for instant delivery, options pricing models were the necessary foundation that enabled options trading to grow from a dozen or so OTC puts and calls advertised by brokers in financial newspapers pre-1973 to the thousands listed for trading at present.
The LLP model, first described in Futures magazine in February 1985, uses market prices for options on commodity futures and equities that basically are valued according to Black-Scholes. The models are not competitive because the LLP program depends on Black-Scholes, expanding its usefulness in several directions including predictive pricing formulas and indications of over- or under-valuation of options market prices.
“Calls on March 2014 softs” (below) shows the LLP model in action. The chart includes calls on five March 2014 softs futures contracts on June 3, 2013, covering futures prices-to-strike price ratios ranging from 0.70 to 1.00.
The height of each options price curve indicates the relative implied volatility attributed by the market to the underlying. For example, calls on coffee and orange juice futures have the highest expected volatility, while cotton and sugar futures are the lowest, and cocoa has midrange implied volatility according to curve heights.
“Softs futures” (below) shows the cumulative price changes for the five March 2014 contracts over the period March 1 to June 3, 2013. It illustrates how call options are priced according to time to expiration and volatility with no directional forecast. For the two higher priced calls — coffee and orange juice —expected volatilities relate to one that has increased by 20% in price while the other has declined by 10%. The lowest options value for cotton futures is supported by a cumulative price change of approximately zero over the three-month period with little up-or-down price variability.