A hybrid method for pricing European options based on multiple assets with transaction costs |
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Authors: | Graziella Pacelli Maria Cristina Recchioni Francesco Zirilli |
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Institution: | 1. 1Instituto di Matematica e Statistica, Universitá di Ancona, Via Pizzecolli 37, 60100 Ancona, Italy;2. 2Dipartimento di Matematica “G. Castelnuovo”, Universitá di Roma “La Sapienza”, Piazzale Aldo Moro 2, 00185 Roma, Italy |
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Abstract: | The problem of pricing European options based on multiple assets with transaction costs is considered. These options include, for example, quality options and options on the minimum of two or more risky assets. The value of these options is the solution of a nonlinear parabolic partial differential equation subject to a final condition given by the payoff function associated with the option. A computationally efficient method to solve this final-value problem is proposed. This method is based on an asymptotic expansion of the required solution with respect to the parameters related to the transaction costs followed by the numerical solution of the linear partial differential equations obtained at each order in perturbation theory. The numerical solution of these linear problems involves an implicit finite-difference scheme for the parabolic equation and the use of the fast Fourier sine transform to solve the resulting elliptic problems. Numerical results obtained on test problems with the method proposed here are shown and discussed. |
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Keywords: | Options Pricing Multiple Assets Transaction Costs Partial Differential Equations Asymptotic Expansion Numerical Method |
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