Mastering Python for Finance - Second Edition

Finite differences in option pricing

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 ...