In this paper, Black Scholes’s pricing model was developed to study American option on future contracts of Brent oil. The practical tests of the model show that market priced option contracts as future contracts less than what model did, which mostly represent option contracts with price rather than without price. Moreover, it suggests call option rather than put option. Using t hypothesis test, price differences were obtained, which can serve as a useful strategy for traders interested in arbitrage practice and risk hedging. This research introduces an optimal strategy (both for call and put option states and buy and sell of future contract ) for all options of buy and sell future contracts with and without price. In this research, six-month data of the end of 2015 about oil option and option of future contracts of North Sea oil for three different maturities were used.
