We develop a lattice-based model to evaluate European and American plain vanilla options when the underlying asset price is driven by a variance gamma process. By applying the Levy-Ito decomposition of the process, we obtain a compound Poisson process made up of a linear drift and the sum of the jumps taken by the process. A multinomial lattice is derived to approximate the compound Poisson process and is used as the corner stone to approximate the evolution of a certain asset price. European and American options are evaluated and, because numerical results show monotonic convergence at the rate of 1/n, we apply a simple two-point Richardson extrapolation and obtain a fast and accurate pricing model.

A fast and accurate lattice model to evaluate options under the variance gamma process / Costabile, Massimo. - In: INTERNATIONAL JOURNAL OF APPLIED MATHEMATICS. - ISSN 1311-1728. - 28:1(2015), pp. 1-22.

A fast and accurate lattice model to evaluate options under the variance gamma process

COSTABILE, Massimo
2015

Abstract

We develop a lattice-based model to evaluate European and American plain vanilla options when the underlying asset price is driven by a variance gamma process. By applying the Levy-Ito decomposition of the process, we obtain a compound Poisson process made up of a linear drift and the sum of the jumps taken by the process. A multinomial lattice is derived to approximate the compound Poisson process and is used as the corner stone to approximate the evolution of a certain asset price. European and American options are evaluated and, because numerical results show monotonic convergence at the rate of 1/n, we apply a simple two-point Richardson extrapolation and obtain a fast and accurate pricing model.
lattice models; variance gamma; Richardson extrapolation
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11770/142348
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