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Here is the example of future option in John Holl's book Options, Futures and Other Derivatives 9th page 384.

I don't understand that when you exercise the future call option, you enter a long position of a future, then what's the price of your future? Actually, I don't much understand the P&L on future when you close out the future after exercise.

For my understand, you hold a long position of future with price $331,$ when you exercise, the price become $330,$ then you should lose the money $$25000\times(331-330)$$ but not earn the money in the book, so where is my misunderstand?

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This goes down to a specificity of options on futures. A future is not a stock, you need to know the entry price to compute the mark-to-market. You can't deliver a future/forward without specifying at which price it was entered. Futures are settled everyday so you will use the last settlement price as the entry price of the delivered future contracts.

Close of August 14th : 330 cents (settlement price of the future, SP)

Spot price on August 15th : 331 cents (spot price of the future, F)

If you exercice a call option on a future contract you receive the future contract + the (positive) difference between strike price and settlement price (10 cents). When you sell the future contract you receive the difference between the settlement price and the spot price (1 cent).

Cash received = (SP - K) + (F - SP) = F - K

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  • $\begingroup$ ok, I may misunderstand the future as forward $\endgroup$
    – A.Oreo
    Commented Aug 14, 2017 at 2:47

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