Picking trees, PDEs or simulation for a pricer

Question

Given a derivative to price, how do you decide which numerical method to use?

Short answer

Match the method to the problem's dimension and features. Finite differences or trees suit low-dimensional problems (one to three factors) and handle early exercise easily, giving accurate greeks. Monte Carlo suits high dimensions and path dependence, since its cost grows mildly with the number of factors, but early exercise needs regression methods and its convergence is slow. Use closed forms or numerical integration (e.g. Fourier methods) whenever the model allows.

Adapted from Wilmott, Frequently Asked Questions in Quantitative Finance, FAQ 28, p.123; question and answer rewritten by SelfMadeQuant.com.

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