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 (in which case, a lookback rate call), the maximum outcome is defined by the “positive” difference between the current market rate and the strike rate. For a put option (specifically, a lookback rate put), the maximum outcome is defined by the “positive” difference between the strike rate and the current market rate.
It is also known as a lookback price option (in case the underlying is an asset price such as a stock price).
