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Pricing multi-asset option problems: a Chebyshev pseudo-spectral method. (English) Zbl 1419.91654

Summary: The aim of this paper is to contribute a new second-order pseudo-spectral method via a non-uniform distribution of the computational nodes for solving multi-asset option pricing problems. In such problems, the prices are required to be as accurately as possible around the strike price. Accordingly, the proposed modification of the Chebyshev-Gauss-Lobatto points would concentrate on this area. This adaptation is also fruitful for the non-smooth payoffs which cause discontinuities in the strike price. The proposed scheme competes well with the existing methods such as finite difference, meshfree, and adaptive finite difference methods on several benchmark problems.

MSC:

91G60 Numerical methods (including Monte Carlo methods)
65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
91G20 Derivative securities (option pricing, hedging, etc.)
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