Search results for "bates model"

showing 3 items of 3 documents

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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Iterative Methods for Pricing American Options under the Bates Model

2013

We consider the numerical pricing of American options under the Bates model which adds log-normally distributed jumps for the asset value to the Heston stochastic volatility model. A linear complementarity problem (LCP) is formulated where partial derivatives are discretized using finite differences and the integral resulting from the jumps is evaluated using simple quadrature. A rapidly converging fixed point iteration is described for the LCP, where each iterate requires the solution of an LCP. These are easily solved using a projected algebraic multigrid (PAMG) method. The numerical experiments demonstrate the efficiency of the proposed approach. Furthermore, they show that the PAMG meth…

ta113Mathematical optimizationStochastic volatilityDiscretizationIterative methodComputer scienceFinite difference methodLinear complementarity problemIterative methodQuadrature (mathematics)Multigrid methodFixed-point iterationBates modelLinear complementarity problemGeneral Earth and Planetary SciencesPartial derivativeAmerican optionGeneral Environmental ScienceProcedia Computer Science
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