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TL;DR

A numerical technique for solving PDEs by discretizing the domain into a grid and approximating derivatives with differences: \( f'(x) \approx \frac{f(x+h) - f(x-h)}{2h} \).

By Valenke Exam Prep Team·Last updated 2026-06-18

Finite Difference Method

A numerical technique for solving PDEs by discretizing the domain into a grid and approximating derivatives with differences: \( f'(x) \approx \frac{f(x+h) - f(x-h)}{2h} \).

Why it matters for interviews

Used to solve the Black-Scholes PDE and its extensions numerically. Finite differences handle American options (early exercise), barrier options, and other cases where closed-form solutions do not exist.

Definition and Mathematical Foundation

A numerical technique for solving PDEs by discretizing the domain into a grid and approximating derivatives with differences: \( f'(x) \approx \frac{f(x+h) - f(x-h)}{2h} \).

Application in Quantitative Finance

Used to solve the Black-Scholes PDE and its extensions numerically. Finite differences handle American options (early exercise), barrier options, and other cases where closed-form solutions do not exist.

Related Terms

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Frequently Asked Questions

What are explicit vs implicit finite difference schemes?▼
Explicit: forward in time, easy to implement but conditionally stable (requires small time steps). Implicit (Crank-Nicolson): unconditionally stable but requires solving a linear system at each step.
How do you handle American option early exercise?▼
At each grid point and time step, compare continuation value (from the PDE) with immediate exercise value. Take the maximum. This creates a free boundary problem naturally handled by finite differences.
What is the Crank-Nicolson scheme?▼
An implicit scheme averaging forward and backward time differences. It is second-order accurate in both time and space, unconditionally stable, and the standard choice for option pricing PDEs.