Path Dependent Greeks

Path dependent Greeks are the risk sensitivities for instruments where the value depends on the sequence of price changes rather than just the terminal state. Unlike vanilla options where Greeks like Delta, Gamma, and Vega are calculated based on current price and time to maturity, path-dependent Greeks must account for the history of the asset.

For example, if an option is close to a barrier, its Delta may spike or drop suddenly, creating a non-linear risk profile. These Greeks are essential for risk managers to understand how their exposure changes as the market evolves.

They help identify potential "cliff" risks where a small change in the underlying price could result in a massive change in the portfolio's risk profile. Modeling these requires advanced simulation techniques such as Monte Carlo methods to capture the path history.