A Greek is a derivative of a price with respect to a market input. When the pricing function is a black box (Monte Carlo, PDE grid, legacy library), the desk bumps the input and forms a finite difference. Truncation error falls as the bump shrinks; roundoff error rises as the bump shrinks — the same tension as conditioning meeting floating-point noise. This note derives forward and central differences from Taylor, states the complex-step idea, and explains why bump size matters for a Greek.
Learning objectives. By the end of this note you should be able to:
- write forward and central difference formulae with leading truncation terms;
- explain the truncation-vs-roundoff trade-off for bump size ;
- state the complex-step derivative formula and when it helps;
- choose and critique an for a one-sided price bump.
In this lesson
- Taylor and finite differences
- Truncation versus roundoff
- Complex-step derivative
- Finance: bumping for a Greek
Before you start
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