Abstract
A new barycentric spectral domain decomposition methods algorithm for solving partial integro-differential models is described. The method is applied to European and butterfly call option pricing problems under a class of infinite activity Levy models. It is based on the barycentric spectral domain decomposition methods which allows the implementation of the boundary conditions in an efficient way. After the approximation of the spatial derivatives, we obtained the semi-discrete equations. The computation of these equations is performed by using the barycentric spectral domain decomposition method. This is achieved with the implementation of an exponential time integration scheme. Several numerical tests for the pricing of European and butterfly options are given to illustrate the efficiency and accuracy of this new algorithm. We also show that Greek options, such as Delta and Gamma sensitivity, are computed with no spurious oscillation.
Highlights
Under jump models, option pricing problems can be modelled by stochastic processes
This paper proposes a study of a barycentric spectral domain decomposition method algorithm for solving Partial-Integro Differential Equations (PIDEs) models related to European and butterfly option pricing problems under a class of infinite activity Levy models
100 CPU time (c) Bull spread call option show the superiority of the SDDM over the FDM, we perform some numerical experiments on the case where Equation (2) is a geometric Brownian motion leading to a standard Black-Scholes equation
Summary
Option pricing problems can be modelled by stochastic processes. Such problems were initially introduced in financial institutions in the late 1960s. Clenshaw Curtis quadrature, shifted Laguerre Gauss quadrature, domain decomposition, partial integro-differential equation, infinite activity Levy processes. Fakharany et al [16] developed an efficient finite difference scheme for partial integro-differential models related to European and American option pricing problems under a wide class of infinity Levy models. This paper proposes a study of a barycentric spectral domain decomposition method algorithm for solving PIDE models related to European and butterfly option pricing problems under a class of infinite activity Levy models. The system of semi-discretised of ordinary differential equations, obtained after approximation of the spatial derivatives using barycentric spectral domain decomposition methods are solved, using an exponential time integration (ETI) scheme. We present some mathematical details of the fundamental approach we use to price European options on infinite activity Levy processes.
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