Because the option valuation models used by financial institutions generate prices that are slightly different from those computed by the LLP formula, it is possible to observe short-term movements of differences between the predicted and actual market prices. The results show that the variations between predicted and actual market prices fall into patterns that have individual characteristics related to specific options and stocks. Examples for corn and crude oil are shown in "Pricing variations" (below).
Prices observed at approximately 5 p.m. on several days indicate variations from the predicted option price curves for September 2011 corn and crude oil futures contracts. On the sample days, corn variations from predicted prices are maintained between plus and minus $3 for 16 strike prices between $6.50 and $7.60. The small differences do not leave much space for a trader to spread price changes between strike prices. Consistency of differences between predicted and actual prices for corn calls suggests an automated trading rule by the market makers: "Keep the price variations between plus and minus $3 of the theoretical price."
More leeway for spread trades is shown in the crude oil variation chart, with price differences from predicted values extending from plus $30 to minus $12. Crude oil futures variations illustrate three possible areas of pricing:
- When strike prices are high relative to the underlying, there is lower trading volume and greater potential for market makers to determine prices within a narrow range around predicted values
- As strike prices are lower compared to the underlying, trading volume increases and there is increased variability around predicted prices, and
- When the underlying price increases toward equality with the strike price, the option pricing model tends to over-price the options and larger negative variations are observed.