Finite difference methods for option pricing

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]

  1. ^ a b Hull, John C. (2002). Options, Futures and Other Derivatives (5th ed.). Prentice Hall. ISBN 978-0-13-009056-0.
  2. ^ a b Schwartz, E. (January 1977). "The Valuation of Warrants: Implementing a New Approach". Journal of Financial Economics. 4: 79–94. doi:10.1016/0304-405X(77)90037-X.
  3. ^ Boyle, Phelim; Feidhlim Boyle (2001). Derivatives: The Tools That Changed Finance. Risk Publications. ISBN 978-1899332885.
  4. ^ Phil Goddard (N.D.). Option Pricing – Finite Difference Methods