Lookback Option Payoffs

Lookback options allow the holder to exercise the contract at the most favorable price achieved by the underlying asset during the life of the option. This feature essentially provides the holder with perfect market timing, as they can look back and select the high or low price.

Due to this significant advantage, lookback options are typically the most expensive type of exotic derivative. Pricing them requires modeling the maximum or minimum distribution of the asset price, which is sensitive to both the volatility and the time horizon.

In crypto, these are rarely used due to the high premium, but they represent the extreme end of path-dependent instruments. Understanding their mechanics helps in grasping how embedded optionality affects liquidity provider returns.