Finite Differences
Approximate derivatives and solve pricing PDEs on a grid.
Define the numerical question and error budget.
Treat the method as an approximation with a measurable error budget. Approximate derivatives and solve pricing PDEs on a grid. Inputs, convergence checks and failure conditions belong beside the output.
Approximate derivatives and solve pricing PDEs on a grid.
Specify the estimator or discretization.
Notation and units
Decimal rates and volatilities, year-fraction time and continuous compounding unless stated otherwise.
Expose convergence and stability conditions.
The numerical target, discretization and stopping rule must be fixed before comparing outputs.
Convergence is assessed against bias, variance or residual tolerances rather than visual smoothness.
Finite precision, boundary treatment and input conditioning can dominate model error.
“An unstated convention is a future reconciliation break.”— THEQUANTBATEMAN
Connect controls to an observable output.
Finite Differences supports Foundations pricing or risk when the numerical target, tolerance and benchmark are explicit. Production use requires convergence evidence and reproducible inputs.
Monitor bias, variance, and failure modes.
Report the Foundations number with its convergence evidence. A stable-looking output can still carry discretization bias or an ill-conditioned input.
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