A buyer does not exercise when exercising would produce no difference or a negative one. For a call, this is when the price of the underlying asset at expiry is at or below the strike price. For a put, it is when the price is at or above the strike price. The buyer's loss is then limited to the premium paid at the start and does not grow further1.

When the price of the underlying asset is exactly equal to the strike price, it makes no difference whether the buyer exercises, but exercising involves costs such as fees, so the option is generally said to be abandoned2.

For the option seller, if the buyer abandons the right, the profit is the premium received2.

Notes

  1. Central Council for Financial Services Information, "3-4 オプション取引の損益" (3-4 Profit and loss of option trading) (in Japanese), the sections on the call buyer and the put buyer. It explains that the buyer abandons the right when the underlying asset is below the strike price (above it for a put) and that the loss is limited to the premium. ↩

  2. The same source (in Japanese): the note below the buyer's table (when the market price equals the strike price, the option is generally abandoned because of fees and other costs) and the section on the call seller (if the buyer abandons the right, the seller's profit is the premium received). ↩ ↩2