We describe some basic finite-difference methods to estimate the derivatives of a generic smooth function. For a function of one variable we provide the derivation of the standard forward difference, backward difference, and central difference approximation of the first and second derivatives. We also derive the expression for the second-order cross partial derivative for a function of two variables. Then we show how to compute the first and second derivative, to the second order, for a smooth function when only non-symmetric displacements in the underlying variable are available. Finally in the appendix we show an example quantitative-finance application to compute the equity-option sensitivities according to different definitions.
Keywords: finite difference,forward difference, backward difference, central difference, local sensitivities, greeks, option-adjusted exposure, vanilla option
Pdf file: finite-difference-methods.pdffinite-difference-methods