Finite Difference Methods

Finite difference methods are numerical techniques used to solve differential equations by approximating them with difference equations. In the context of derivatives, they are used to solve the Black-Scholes partial differential equation to find the value of an option.

By discretizing the price and time dimensions into a grid, these methods calculate the option value at each point. This approach is highly effective for American-style options, where the holder can exercise at any time before expiration.

It allows for the inclusion of boundary conditions that represent early exercise or other constraints. In crypto, finite difference methods are used for pricing options on protocols that allow for flexible exercise conditions.

They offer a stable and deterministic alternative to simulation-based methods for certain types of problems. The precision of the result is determined by the density of the grid used in the calculation.

It is a reliable tool for desks that require consistent and repeatable pricing.