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

The European-style option’s payoff is defined as the amount by which the underlying asset price at expiration has subceeded below (fallen short of) the highest asset price achieved during the option life.

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