A lookback option that gives its holder the right, without the obligation, to buy at the lowest price the underlying achieved over the lookback period. For example, the buyer (holder) of a lookback call on a share of stock XYZ has the right to purchase a certain number of shares at the lowest price realized between the creation of the call and its expiration date.

The European-style option’s payoff is defined as the amount by which the underlying asset price at expiration has exceeded the lowest asset price achieved during the option life.

A lookback call has many variations including American lookback call, European lookback call, floating strike lookback call, etc.