A look back option is a path dependent option settles based upon the maximum or minimum underlier value achieved during the entire life of the option. Essentially, at expiration, the holder can "look back" over the life of the option and exercise based upon the optimal underlier value achieved during that period. Lookbacks can be structured as puts or calls and come in two basic forms:

A fixed strike lookback option is cash settled and has a strike set in advance. It is exercised based upon the optimal underlier value achieved during the life of the option. In the case of a call, this is the highest underlier value achieved, so the call has a payoff equal to the greater of: zero or the difference between that highest value and the fixed strike. In the case of a put, the optimal value is the lowest underlier value achieved, and the payoff is the greater of: zero or the difference between the strike and that lowest value.

A floating strike lookback option can have cash or physical settled. It settles based upon a strike that is set equal to the optimal value achieved by the underlier over the life of the option. In the case of a call, that optimal value is the lowest value achieved by the underlier, so the call has a payoff equal to the difference between the value of the underlier at expiration and the lowest value achieved by the underlier over the life of the option. In the case of a put, the payoff is the difference between the highest value achieved by the underlier and the value of the underlier at expiration.

Lookback options have obvious appeal, but they are expensive. Their structure doesn't mimic typical business liabilities, so they are largely a speculative device.