Path-Dependent Options
Asians, barriers, and lookbacks — when the path matters as much as the endpoint
A vanilla European option's payoff depends on a single number: the underlying's price at the moment of expiration. Whatever the stock did between contract initiation and expiration is irrelevant to the payoff function. The contract is, in formal terms, path-independent — only the endpoint matters.
A large class of contracts in commodity, foreign-exchange, and structured-product markets has the opposite feature: the payoff function references information about the underlying's full path, not just its terminal value. Path-dependent options are the technical name for this family. The three canonical structures are Asian options (payoff based on average price), barrier options (payoff conditional on hitting or not hitting a level), and lookback options (payoff based on the max or min reached during the contract period).
All three are widely used by sophisticated end-users — energy companies hedging average-realized prices, treasuries hedging multi-month FX exposures, and structured-product issuers building yield-enhanced retail products — but rarely traded in vanilla retail option chains.
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What this lesson covers
- 1The reference Asian option — averaging dampens the payoff variance
- 2Lookback options — payoff at the path's extreme
- 3Path-Dependent Option Pricer
- 4Pricing identities for path-dependent contracts
- 5Path-dependent option pricing reference (S=$200, K=$200, T=30 days, σ=30%, r=4.5%)
- 6Dated Brent and crude-oil Asians — the structural reason commodity buyers need average-rate options
- 7Where to see this on the platform
- 8Summary