Finite-Difference Checks for Greeks
Finite differences approximate sensitivities numerically and provide an independent check on analytic Greeks.
Explanation
Analytic Greeks are derivatives of the pricing formula; finite differences approximate them by bumping inputs and re-pricing.
Central differences, using up and down bumps, usually give better accuracy than one-sided bumps for smooth payoffs.
Choosing the bump size involves a trade-off: too small leads to numerical noise, too large breaks the linear approximation.
For Monte Carlo pricers, using common random numbers across bumps reduces sampling noise in the finite-difference estimate.
greeksfinite differencessensitivitieschecks
Interactive visualisation
Finite-difference checks for Greeks
Bump-and-reprice provides an independent check on analytic sensitivities.
S
100
K
100
r
0.020
vol
0.25
T
1.00
Finite difference
bump h
0.50
Monte Carlo noise (optional)
paths
2000
noise
1.0
seed
42
Call price
10.87056
Analytic delta
0.581214
FD delta
0.581197
|FD − analytic|
0.000017
Error vs bump size
Interpretation
- Central differences usually dominate forward differences for smooth payoffs.
- Bump choice is a trade-off: numerical noise versus curvature bias.
- With Monte Carlo, CRN reduces noise in the difference by correlating bumps.