Double Spiral Method, Gamma Transform and Pricing Arithmetic Asian Options

29 Pages Posted: 23 Aug 2016

Date Written: August 20, 2016

Abstract

A backward induction procedure for pricing arithmetic Asian options in Levy models is realized in the dual space. Each step of the procedure is the composition of a multiplication operators by an explicitly given function, and the convolution operator ${\cal H}_\Ga$, which belongs to a class of natural generalizations of the Hilbert transform ${\cal H}$. The kernel of ${\cal H}_\Ga$ being $(1/2\pi )^{-1}\Ga(i(\eta-\xi))$, we call ${\cal H}_\Ga$ the Gamma transform. An efficient realization of the procedure (Double-Spiral method) is based on calculations of the functions on two parallel lines, using the fast convolution.

Keywords: Arithmetic Asian Options, Hilbert Transform, Generalized Hilbert Transform, Gamma Transform, Double Spiral Method, Fast Convolution, Fast Hilbert Transform

JEL Classification: C02, C65

Suggested Citation

Levendorskii, Sergei Z., Double Spiral Method, Gamma Transform and Pricing Arithmetic Asian Options (August 20, 2016). Available at SSRN: https://ssrn.com/abstract=2827138 or http://dx.doi.org/10.2139/ssrn.2827138

Sergei Z. Levendorskii (Contact Author)

Calico Science Consulting ( email )

Austin, TX
United States

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