Fast Pricing and Calculation of Sensitivities of OTM European Options Under Levy Processes

44 Pages Posted: 14 Apr 2010 Last revised: 28 Sep 2010

See all articles by Sergei Levendorskii

Sergei Levendorskii

Calico Science Consulting

Jiayao Xie

affiliation not provided to SSRN

Date Written: September 27, 2010

Abstract

Fast Fourier transform (FFT) method is now a standard calibration engine. However, in many situations, such as pricing of deep out-of-the-money European options, FFT produces large errors. We propose fast and accurate realizations of Integration-Along-Cut method (IAC method), which explicitly control the error of pricing OTM options. For one strike (and OTM options), IAC is significantly faster than FFT-based methods. Even if prices for many strikes are needed, IAC method, together with quadratic interpolation, successfully competes with CONV method developed by Lord et. al., the COS method suggested by Fang and Oosterlee, the saddlepoint method suggested by Carr and Madan, and the refined and enhanced versions of FFT recently suggested by M.~Boyarchenko and Levendorskii. For calculations of sensitivities, a relative advantage of IAC is even greater. The method is applicable to a wide class of Levy-driven models, KoBoL processes (a.k.a. CGMY model) of finite variation, Variance Gamma processes and Normal Inverse Gaussian processes including.

Keywords: Option pricing, sensitivities, Fast Fourier transform, refined and enhanced Fast Fourier transform, Integration-along-cut method, Levy processes, Normal Inverse Gaussian model, Variance Gamma model, KoBoL, CGMY, out-of-the-money options

JEL Classification: C63

Suggested Citation

Levendorskii, Sergei Z. and Xie, Jiayao, Fast Pricing and Calculation of Sensitivities of OTM European Options Under Levy Processes (September 27, 2010). Available at SSRN: https://ssrn.com/abstract=1589809 or http://dx.doi.org/10.2139/ssrn.1589809

Sergei Z. Levendorskii (Contact Author)

Calico Science Consulting ( email )

Austin, TX
United States

Jiayao Xie

affiliation not provided to SSRN

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