Path Dependent Options

Derivation

The valuation and payoff structure of these options are intrinsically linked to the entire sequence of the underlying asset’s price path between initiation and expiration, not just the final price. This dependency means that intermediate price levels, such as hitting a specific barrier or achieving a local maximum, directly influence the contract’s final value or exercise possibility. Such path-sensitivity necessitates specialized numerical methods for accurate pricing.
Rho A stylized depiction of a decentralized finance protocol's inner workings.

Rho

Meaning ⎊ Sensitivity of an options price to changes in the risk free interest rate.