exotic options

Exotic options have path-dependent payoffs — their value depends on the entire price history, not just the final price. No closed-form solutions exist, making Monte Carlo the primary pricing method.

Asian: payoff = max(avg(S) − K, 0) · Barrier: knocked out if S hits B · Lookback: payoff = S_T − min(S)

Asian options smooth out manipulation risk. Barrier options are cheaper than vanilla. Lookback options give perfect hindsight — and cost accordingly.