Finite difference schemes are very much similar to trinomial tree option pricing, where each node is dependent on three other nodes with an up movement, a down movement, and a flat movement. The motivation behind the finite differencing is the application of the Black-Scholes Partial Differential Equation (PDE) framework (involving functions and their partial derivatives), where price S(t) is a function of f(S,t), with r as the risk-free rate, t as the time to maturity, and σ as the volatility of the underlying security:
The finite difference technique tends to converge faster than lattices and approximates complex exotic options very well.
To solve a PDE by finite differences working backward in time, a discrete-time grid of size M by N is set up to reflect asset prices over a course of time, so that S and t take on the following...
