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: Suggested Citation