Michael Brenndoerfer | Data & AI, Private Equity, Technology

Michael Brenndoerfer

Finite Difference Methods for Option Pricing › Key Parameters

Michael BrenndoerferDecember 4, 20251 min read

Quantitative FinanceAll chapters

Part 6 of 15Numerical Methods for Derivative Pricing

Chapter 36Finite Difference Methods for Option Pricing › Key Parameters

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The key parameters for finite difference option pricing are:

S: Current stock price. Represents the underlying asset value at any grid point.
K: Strike price. Determines the option payoff at expiration and intrinsic value.
T: Time to expiration. The domain over which the PDE is solved.
r: Risk-free interest rate. Used for drift in the PDE and discounting.
$\sigma$ : Volatility. Determines the diffusion coefficient in the Black-Scholes PDE.
M: Number of price steps. Determines spatial resolution ( $ΔS$ ).
N: Number of time steps. Determines temporal resolution ( $Δt$ ) and stability.