Finite difference methods for option pricing are numerical methods used in mathematical finance for the valuation of options.[1] Finite difference methods were first applied to option pricing by Eduardo Schwartz in 1977.[2][3]: 180
In general, finite difference methods are used to price options by approximating the (continuous-time) differential equation that describes how an option price evolves over time by a set of (discrete-time) difference equations. The discrete difference equations may then be solved iteratively to calculate a price for the option.[4] The approach arises since the evolution of the option value can be modelled via a partial differential equation (PDE), as a function of (at least) time and price of underlying; see for example the Black–Scholes PDE. Once in this form, a finite difference model can be derived, and the valuation obtained.[2]
The approach can be used to solve derivative pricing problems that have, in general, the same level of complexity as those problems solved by tree approaches.[1]