How do lookback options work with minimum and maximum references?

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AcadiFi · Accepted Answer

A lookback option gives the holder the benefit of the most favorable underlying price observed during the option's life. Two main variants exist: floating-strike and fixed-strike lookbacks.

A floating-strike lookback call pays the terminal price minus the minimum observed price over the life — effectively letting you buy at the lowest point. A floating-strike lookback put pays the maximum observed minus the terminal — letting you sell at the peak. These payoffs are never negative.

A fixed-strike lookback call has a preset strike K and pays the maximum observed price minus K, capped at zero from below. A fixed-strike lookback put pays K minus the minimum observed price.

Example: trader Ignacio Valenzuela at Palo Verde Derivatives writes a floating-strike lookback call on Arkwright Pharmaceuticals. Over the six-month life, the stock ranges from 42 to 68 and ends at 61. Payoff equals 61 minus 42 equals 19 dollars. A vanilla call struck at 50 would have paid only 11.

Because lookbacks always pick the best price in hindsight, they are the most expensive path-dependent options. Premiums can easily be two to three times the vanilla equivalent. They are priced using continuous-monitoring closed forms under Black-Scholes assumptions (Goldman-Sosin-Gatto formulas) or Monte Carlo for discrete monitoring. They are rarely traded on exchanges due to their cost but appear in employee stock incentive plans and structured retail products.

How do lookback options work with minimum and maximum references?

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