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Operator splitting methods for American option pricing. (English) Zbl 1063.65081

Summary: We propose operator splitting methods for solving the linear complementarity problems arising from the pricing of American options. The space discretization of the underlying Black-Scholes equation is done using a central finite-difference scheme. The time discretization as well as the operator splittings are based on the Crank-Nicolson method and the two-step backward differentiation formula. Numerical experiments show that the operator splitting methodology is much more efficient than the projected successive overrelaxation, while the accuracy of both methods are similar.

MSC:

65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
91G60 Numerical methods (including Monte Carlo methods)
35K15 Initial value problems for second-order parabolic equations
91G20 Derivative securities (option pricing, hedging, etc.)
60G40 Stopping times; optimal stopping problems; gambling theory

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References:

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