Alternating Direction Implicit Finite Element Method for Multi-Dimensional Black-Scholes Models

DOI10.4208/aamm.OA-2018-0144zbMath1488.65435WikidataQ128347390 ScholiaQ128347390MaRDI QIDQ5156663

A. V. Lapin, Shuhua Zhang, Li-Mei Li

Publication date: 11 October 2021

Published in: Advances in Applied Mathematics and Mechanics (Search for Journal in Brave)

zbMATH Keywords

finite element methodalternating direction methodsemi-implicit approximationBlack-Scholes models

Mathematics Subject Classification ID

Numerical methods (including Monte Carlo methods) (91G60) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) 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) Finite difference methods for boundary value problems involving PDEs (65N06) PDEs in connection with game theory, economics, social and behavioral sciences (35Q91)

Related Items (1)

Modulus-based successive overrelaxation iteration method for pricing American options with the two-asset Black-Scholes and Heston's models based on finite volume discretization

Cites Work

• The Pricing of Options and Corporate Liabilities
• Option pricing with a direct adaptive sparse grid approach
• A robust and accurate finite difference method for a generalized Black-Scholes equation
• Optimal error estimates for linear parabolic problems under minimal regularity assumptions
• Adaptive \(\theta \)-methods for pricing American options
• A comparison study of ADI and operator splitting methods on option pricing models
• A general formulation of alternating direction methods. I: Parabolic and hyperbolic problems
• Far Field Boundary Conditions for Black--Scholes Equations
• COMPARISON OF NUMERICAL SCHEMES ON MULTI-DIMENSIONAL BLACK-SCHOLES EQUATIONS
• The Numerical Solution of Parabolic and Elliptic Differential Equations
• Computational techniques for basic affine models of portfolio credit risk
• Optimal $H^{p,{p/2}} $ Error Estimates for a Parabolic Galerkin Method
• Error Estimates for Semidiscrete Finite Element Approximations of Linear and Semilinear Parabolic Equations Under Minimal Regularity Assumptions
• Computational Methods for Option Pricing
• A high-order front-tracking finite difference method for pricing American options under jump-diffusion models
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