Search results for "finite difference method"

showing 3 items of 63 documents

Reduced Order Models for Pricing European and American Options under Stochastic Volatility and Jump-Diffusion Models

2017

Abstract European options can be priced by solving parabolic partial(-integro) differential equations under stochastic volatility and jump-diffusion models like the Heston, Merton, and Bates models. American option prices can be obtained by solving linear complementary problems (LCPs) with the same operators. A finite difference discretization leads to a so-called full order model (FOM). Reduced order models (ROMs) are derived employing proper orthogonal decomposition (POD). The early exercise constraint of American options is enforced by a penalty on subset of grid points. The presented numerical experiments demonstrate that pricing with ROMs can be orders of magnitude faster within a give…

ta113Mathematical optimizationGeneral Computer ScienceStochastic volatilityDifferential equationEuropean optionMonte Carlo methods for option pricingJump diffusion010103 numerical & computational mathematics01 natural sciencesTheoretical Computer Science010101 applied mathematicsValuation of optionsModeling and Simulationlinear complementary problemRange (statistics)Asian optionreduced order modelFinite difference methods for option pricing0101 mathematicsAmerican optionoption pricingMathematicsJournal of Computational Science
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Reduced Order Models for Pricing American Options under Stochastic Volatility and Jump-diffusion Models

2016

American options can be priced by solving linear complementary problems (LCPs) with parabolic partial(-integro) differential operators under stochastic volatility and jump-diffusion models like Heston, Merton, and Bates models. These operators are discretized using finite difference methods leading to a so-called full order model (FOM). Here reduced order models (ROMs) are derived employing proper orthogonal decomposition (POD) and non negative matrix factorization (NNMF) in order to make pricing much faster within a given model parameter variation range. The numerical experiments demonstrate orders of magnitude faster pricing with ROMs. peerReviewed

ta113Mathematical optimizationStochastic volatilityDiscretizationComputer scienceJump diffusionFinite difference method010103 numerical & computational mathematics01 natural sciencesNon-negative matrix factorization010101 applied mathematicsValuation of optionslinear complementary problemRange (statistics)General Earth and Planetary SciencesApplied mathematicsreduced order modelFinite difference methods for option pricing0101 mathematicsAmerican optionoption pricingGeneral Environmental ScienceProcedia Computer Science
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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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