Exotic Options

Exotic options have non-standard payoffs that depend on the path of the underlying, not just its value at expiry.

Asian options pay based on the average price over a window, not the terminal price. They're cheaper than vanillas and reduce manipulation risk near expiry — common in commodity markets.

Barrier options activate (knock-in) or extinguish (knock-out) when the underlying crosses a level. They're cheaper than vanillas and let buyers express more specific views.

Lookback options pay based on the maximum or minimum price during the period — typically expensive, but they remove timing risk for the buyer.

Digital (binary) options pay a fixed amount if a condition is met, zero otherwise. They have discontinuous payoffs that make hedging tricky — the gamma blows up near the strike at expiry.

Pricing exotics generally requires Monte Carlo or PDE methods because closed forms rarely exist. Hedging is complicated by the path-dependence: simple delta-vega hedging often isn't enough.