when using a floating strike lookback option the strike price is set automatically at maturity to the most favorable underlying price reached during the contract s life call options fix the strike at the lowest underlying asset price adversely put options fix the strike at the highest price point the option will then settle against the market price calculating the profit or loss against the floating strike 
the fixed strike option solves the market exit problem the best time to get out the floating strike solves the market entry problem the best time to get in examples of lookback optionsin example number one if you assume a stock trades at 50 at both the start and end of the three month option contract so there is no net change gain or loss the path of the stock will be the same for both the fixed and floating strike versions at one point during the life of the option the highest price is 60 and the lowest price is 40 the profit is the same because the stock moved the same amount higher and lower during the life of the option in example number two let s assume the stock had the same high of 60 and low of 40 but closed at the end of the contract at 55 for a net gain of 5 finally in example number three let s assume the stock closed at 45 for a net loss of 5 