Introduction to Finite Difference Methods for Option Pricing

Finite-difference methods is the generic term for a large number of techniques that can be used for solving differential equations, approximating derivatives with finite differences.

It consists of a discretization of both spatial (underlying price in our case) and time intervals to obtain a finite grid.

We find solutions for a differential equation by approximating every partial derivative with numerical methods and we apply the solution to the points of the grid.

This numerical method is very useful in finance to solve partial differential equations (PDE) which model the evolution of option prices, such as the Black-Scholes PDE.

The three main methods are:

– the explicit method which goes backward

– the implicit method which goes forward

– the Crank-Nicolson method which is an average of the two

The explicit method is equivalent to a trinomial tree approach, it is easy to formulate but it can be unstable, requiring an important number of time steps to avoid stability issues.

The Implicit and Crank-Nicolson are stable ones, but more complex to formulate requiring the use of matrix calculations, the later one being the most efficient with a faster rate of convergence.

Presentation

Save 10% on All Quant Next Courses with the Coupon Code: QuantNextBlog10

For students and graduates: We offer a 50% discount on all courses, please contact us if you are interested: contact@quant-next.com