Search results for "Operator splitting method"

showing 3 items of 3 documents

Operator splitting methods for American option pricing

2004

Abstract 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 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 SOR, while the accuracy of both methods are similar.

Backward differentiation formulaMathematical optimizationPartial differential equationDiscretizationApplied MathematicsFinite difference methodSemi-elliptic operatorTime discretizationValuation of optionsComplementarity theoryLinear complementarity problemCrank–Nicolson methodOperator splitting methodAmerican optionMathematicsApplied Mathematics Letters
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ADI schemes for valuing European options under the Bates model

2018

Abstract This paper is concerned with the adaptation of alternating direction implicit (ADI) time discretization schemes for the numerical solution of partial integro-differential equations (PIDEs) with application to the Bates model in finance. Three different adaptations are formulated and their (von Neumann) stability is analyzed. Ample numerical experiments are provided for the Bates PIDE, illustrating the actual stability and convergence behaviour of the three adaptations.

DiscretizationStability (learning theory)bates modelBATES010103 numerical & computational mathematicsalternating direction implicit schemes01 natural sciencessymbols.namesakeConvergence (routing)FOS: MathematicsApplied mathematicsMathematics - Numerical Analysis0101 mathematicsAdaptation (computer science)Mathematicsta113Numerical Analysispartial integro-differential equationsApplied MathematicsNumerical Analysis (math.NA)stability010101 applied mathematicsComputational MathematicsAlternating direction implicit methodsymbolsoperator splitting methodsMathematicsVon Neumann architectureApplied Numerical Mathematics
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ADI schemes for valuing European options under the Bates model

2018

This paper is concerned with the adaptation of alternating direction implicit (ADI) time discretization schemes for the numerical solution of partial integro-differential equations (PIDEs) with application to the Bates model in finance. Three different adaptations are formulated and their (von Neumann) stability is analyzed. Ample numerical experiments are provided for the Bates PIDE, illustrating the actual stability and convergence behaviour of the three adaptations. peerReviewed

partial integro-differential equationsbates modelalternating direction implicit schemesstabilityoperator splitting methods
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