Reduced Basis Methods for Pricing Options with the Black--Scholes and Heston Models

DOI10.1137/140981216zbMath1335.91099arXiv1408.1220OpenAlexW1649019767MaRDI QIDQ2941477

Julien Salomon, O. Burkovska, Bernard Haasdonk, Barbara I. Wohlmuth

Publication date: 28 August 2015

Published in: SIAM Journal on Financial Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1408.1220

zbMATH Keywords

option pricingmodel reductiona posteriori error estimationreduced basis methods

Mathematics Subject Classification ID

Numerical methods (including Monte Carlo methods) (91G60) Unilateral problems for linear parabolic equations and variational inequalities with linear parabolic operators (35K85) Derivative securities (option pricing, hedging, etc.) (91G20) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) PDEs in connection with game theory, economics, social and behavioral sciences (35Q91) Numerical methods for variational inequalities and related problems (65K15)

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Cites Work

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• The Pricing of Options and Corporate Liabilities
• Stability of the SUPG finite element method for transient advection-diffusion problems
• Calibration of options on a reduced basis
• Operator splitting methods for pricing American options under stochastic volatility
• Penalty methods for American options with stochastic volatility
• Computational methods for quantitative finance. Finite element methods for derivative pricing
• A Reduced Basis Method for the Simulation of American Options
• A prioriconvergence of the Greedy algorithm for the parametrized reduced basis method
• Projection‐based model reduction for contact problems
• A Reduced Basis for Option Pricing
• A posteriori error estimator and error control for contact problems
• On the solution of complementarity problems arising in American options pricing
• Variationally consistent discretization schemes and numerical algorithms for contact problems
• Reduced basis for vanilla and basket options
• The Primal-Dual Active Set Strategy as a Semismooth Newton Method
• A Mortar Finite Element Method Using Dual Spaces for the Lagrange Multiplier
• An Introduction to Variational Inequalities and Their Applications
• Multiscale methods for the valuation of American options with stochastic volatility
• A Reduced Basis Method for Parametrized Variational Inequalities
• Mixed Finite Element Methods and Applications
• On Noncoercive Variational Inequalities
• Convergence Rates of the POD–Greedy Method
• A posteriorierror bounds for reduced-basis approximations of parametrized parabolic partial differential equations
• Computational Methods for Option Pricing
• Learning the parts of objects by non-negative matrix factorization
• A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options
• Numerical techniques for the valuation of basket options and their Greeks
• Efficient numerical methods for pricing American options under stochastic volatility
• Reduced basis method for finite volume approximations of parametrized linear evolution equations
• ADI finite difference schemes for option pricing in the Heston model with correlation
• Tools for computational finance