Fast Calculation of Prices and Sensitivities of European Options Under Variance Gamma

46 Pages Posted: 24 Aug 2011 Last revised: 30 Jan 2012

See all articles by Marco de Innocentis

Marco de Innocentis

Credit Suisse Securities (Europe) Limited; University of Leicester

Date Written: August 24, 2011

Abstract

We present new, fast and accurate methods to calculate the prices and sensitivities of European vanilla and digital options under the Variance Gamma model, and the Variance Gamma PDF. For ATM and near-ATM options with short times to maturity, they are usually much faster than methods based on the (inverse) Fourier transform. We show that interpolation near ATM can be very inaccurate, especially for digitals, whereas the results calculated with our method agree with the benchmarks obtained with the most efficient iFT algorithm.

Keywords: European option pricing, Levy processes, Variance Gamma, VG, KoBoL, CGMY, ATM, inverse Fourier Transform, FFT, flat iFT, parabolic iFT, hyperbolic iFT, ATMVG, FastVG, model calibration

JEL Classification: G12, C63

Suggested Citation

de Innocentis, Marco, Fast Calculation of Prices and Sensitivities of European Options Under Variance Gamma (August 24, 2011). Available at SSRN: https://ssrn.com/abstract=1916020 or http://dx.doi.org/10.2139/ssrn.1916020

Marco De Innocentis (Contact Author)

Credit Suisse Securities (Europe) Limited ( email )

1 Cabot Square
London, E14 4QJ
United Kingdom

University of Leicester ( email )

Department of Mathematics
University Road
Leicester, LE1 7RG
United Kingdom

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