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Risky Measures of Risk: Error Analysis of Numerical Differentiation

80 Pages Posted: 9 Jan 2007  

Harvey J. Stein

Bloomberg L.P.; Columbia University - Department of Mathematics

Date Written: June 22, 2005

Abstract

We review and detail the causes of errors in numerical differentiation, including roundoff error, convexity error, cancellation error and correlated errors. We discuss methods for improving accuracy, including step size selection and smoothing techniques, as well as a number of approaches specific to the types of computations being done.

Keywords: greeks, delta, gamma, theta, differentiation, numerical, numerical differentiation, error, error control, roundoff, convexity, cancellation, smoothing, Hermite, filtering, convolution, Fourier, Gaussian, quadrature, Complex

JEL Classification: C63, G13

Suggested Citation

Stein, Harvey J., Risky Measures of Risk: Error Analysis of Numerical Differentiation (June 22, 2005). Available at SSRN: https://ssrn.com/abstract=955724 or http://dx.doi.org/10.2139/ssrn.955724

Harvey J. Stein (Contact Author)

Bloomberg L.P. ( email )

731 Lexington Avenue
New York, NY 10022
United States
212 617 3059 (Phone)

Columbia University - Department of Mathematics ( email )

New York, NY
United States

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