A lookback option whose payoff (and performance), at expiration (for a European version) or over its lifetime (for an American version) depends on the maximum rate (e.g., an exchange rate) realized over the option’s life (from the perspective of an option holder), after adjusting for the strike price (strike rate). For a call option, the maximum outcome is defined by the “positive” difference between the current market rate and the strike rate:

Max _0≤s≤T [(S_s – K), O]

Where: S_s is the current market rate, K is the strike rate, T is time to maturity, s any point in time over an option’s time to maturity.