What it means
A standard option pays out based on where the price ends up on the expiry date. A lookback option instead records the highest or lowest price during a set period, and uses that figure in the payoff.
This removes the regret of picking the wrong moment to buy or sell. There are two main types.
A floating-strike lookback call lets the holder buy at the lowest price seen during the life of the option, so the payoff is the final price minus that minimum. A floating-strike lookback put lets the holder sell at the highest price seen, and pays that maximum minus the final price.
A fixed-strike lookback works differently. The strike price is set in advance, but the payoff is based on the most favourable price reached.
A fixed-strike lookback call pays the maximum price seen minus the strike, if positive. Because the holder can never do worse than at expiry and often does better, the premium is substantially higher than for a regular option.
Pricing relies on mathematical models that account for the whole path of the price and the volatility assumed, so dealers quote them over the counter rather than on an exchange. Companies and investors use them in specialised settings, for example to hedge an uncertain timing of a purchase or to give employees or clients a product with a built-in best-price feature.
They are also a common teaching example of path-dependent options (options whose value depends on the route the price takes, not just where it ends). Dealers usually hedge the risk of selling a lookback by trading the underlying asset frequently, and the cost of doing so is built into the price.
Because the payoff is so sensitive to extreme prices, small changes in assumed volatility can move the premium significantly. Buyers should therefore ask what volatility the quote assumes and how often prices are sampled.
In practice
Real-world examples.
Example
A fund that expects a currency to be volatile buys a lookback call, so it can effectively buy at the lowest exchange rate seen over six months. It pays a higher premium for that flexibility.
Example
A manufacturer uses a lookback put on a metal it sells, so it receives the highest price reached during the quarter rather than whatever price prevails on the sales date. The finance team weighs the extra premium against the revenue it can lose when it sells at a poor moment.
Example
A bank issues a structured note to clients with a lookback feature, promising a payoff linked to the best level of an index during a one-year period. Clients like the idea of capturing the peak, although the bank prices in a lower participation rate to pay for the feature.
Formula
Calculation
Floating-strike lookback call payoff = Final price - Minimum price during the life
Fixed-strike lookback call payoff = Maximum price during the life - Strike price (not below zero)
Suppose an investor holds a floating-strike lookback call on 1,000 shares of a commodity-linked stock, and the share starts at $90.
During the life of the option the lowest price reached is $80, and the price at expiry is $95.
Payoff per share = $95 - $80 = $15.
Total payoff = $15 x 1,000 = $15,000.
A standard call struck at $90 would have paid only $95 - $90 = $5 per share, or $5,000, so the lookback pays $10,000 more but costs more to buy.Case study
Seen in the real world.
Greenfield Fuel Supplies is an illustrative, fictional distributor that buys diesel in large batches and cannot predict the best moment to buy. The treasurer was tired of watching prices drop shortly after each purchase, so she asked a bank about a lookback option.
The bank offered a floating-strike lookback call on 500,000 gallons over three months. The premium was $0.18 per gallon, about double the price of a conventional option, because the bank would pay out against the lowest price in the window.
Prices fell to $2.60 and then rose to $3.00 by expiry, so the option paid $0.40 per gallon, or $200,000, against the premium of $90,000. In this fictional example the lookback paid off, but the treasurer noted that if prices had simply risen throughout, the minimum price would have been the starting price and the option would have recovered much less than its cost.
Watch out
Common mistakes.
- Believing a lookback option guarantees a profit, when the premium is high and the payoff can still be lower than the cost.
- Comparing its premium with an ordinary option and assuming it is overpriced, when the extra cost reflects the extra value of the best-price feature.
- Ignoring how the price is monitored, for example daily closing prices versus continuous prices, which changes the payoff.
Questions
People also ask.
Why are lookback options expensive?
Because the holder gets the best price in hindsight, which guarantees a payoff at least as large as that of a standard option.
Are lookback options traded on exchanges?
Mostly not. They are usually traded over the counter between banks and clients, with terms agreed individually.
What does path-dependent mean?
It means the payoff depends on the prices along the way, not just the final price on the expiry date.
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