A lookback option pays on the extremum of the path — the maximum or minimum stock price over the life of the contract. It is the purest "buy the low, sell the high" structured product: a floating-strike call delivers , locking in the best purchase price retrospectively. Under GBM with continuous monitoring, closed-form prices exist built on the same reflection principle that powers continuous barrier formulas. This note classifies fixed vs floating lookbacks, states the floating-strike formulas, explains the fixed-strike reduction via a put–call parity argument, and names the discrete-max bias that bites every tree and Monte Carlo implementation.
Learning objectives. By the end of this note you should be able to:
- write payoffs for fixed and floating lookback calls and puts;
- explain how the reflection principle prices path extrema under GBM;
- quote the Hull formula for a newly issued floating lookback call and interpret its terms;
- derive fixed-strike lookbacks from modified floating-strike prices;
- state the direction of discrete-monitoring bias for simulated extrema.
In this lesson
- Contract taxonomy
- Continuous monitoring and the reflection principle
- Floating-strike formulas (newly issued)
- Fixed-strike lookbacks via put–call parity
- Discrete monitoring bias
- Computation summary
Before you start
The full lesson, with worked examples and exercise solutions, is for members.
Read the full lessonNew to SelfMadeQuant.com? See membership options or browse the Derivatives Pricing and Computational Finance syllabus.