Volatilities derived from calculations on the options market are expected to be ranked the same by Black-Scholes and LLP, because both models are based on the price range forecasts implied by current put and call prices.
“Volatility comparison” (below) shows how the two models compute volatilities for the set of calls on softs futures on June 3, 2013. The percentages are heights of call price curves measured by the LLP model at the point where the futures price equals the strike price, compared at each expiration date with the Black-Scholes standard deviation.
“Dollar variations: Price curves” (below) shows another potential trading technique provided by the LLP pricing model. For the March 2014 calls on softs futures, the difference from the call price curve is computed. All but the coffee calls have price variations peaking at approximately $20 while the highest variation for March 2014 coffee calls is $87.
Of course, the variations shift continuously and any trade based on specific dollar amounts should be based on a longer-term comparison. In this case, selling the 170 strike at 4.73 ($1,773.75) while buying the 210 strike at 1.80 ($675) on June 3 would have resulted in a gain on June 7. The 170 strike would be bought at 4.32 ($1,620) as the high dollar variation declined, while the 210 strike was sold at 1.56 ($585.00) for a net gain of $63.75.
Having two options pricing models that are compatible with each having special abilities in terms of estimating underlying volatilities, recommending spreads between strike prices and expirations, and computing pricing equations would seem to have definite advantages. As indicated by the softs futures example, there are many interesting and potentially profitable aspects revealed by closer inspection of the Black-Scholes and LLP models.
Paul Cretien is an investment analyst and financial case writer. His e-mail is PaulDCretien@aol.com.