A FAST, STABLE AND ACCURATE NUMERICAL METHOD FOR THE BLACK–SCHOLES EQUATION OF AMERICAN OPTIONS

DOI10.1142/S0219024908004890zbMath1185.91175MaRDI QIDQ3527432

Ronald E. Mickens, Matthias Ehrhardt

Publication date: 29 September 2008

Published in: International Journal of Theoretical and Applied Finance (Search for Journal in Brave)

zbMATH Keywords

finite difference methodfree boundary problemoption pricingBlack-Scholes equationAmerican optionartificial boundary conditioncomputational finance

Mathematics Subject Classification ID

Numerical methods (including Monte Carlo methods) (91G60) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Derivative securities (option pricing, hedging, etc.) (91G20)

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Cites Work

• The Pricing of Options and Corporate Liabilities
• Convergence of difference scheme for heat equation in unbounded domains using artificial boundary conditions
• Discrete artificial boundary conditions for nonlinear Schrödinger equations
• Accurate and efficient pricing of vanilla stock options via the Crandall-Douglas scheme.
• A class of artificial boundary conditions for heat equation in unbounded domains
• A two-step simulation procedure to analyze the exercise features of American options
• Option pricing with Mellin transforms
• Compact finite difference method for American option pricing
• Discrete transparent boundary conditions for parabolic systems
• A new direct method for solving the Black-Scholes equation
• Fast calculation of energy and mass preserving solutions of Schrödinger-Poisson systems on unbounded domains
• Discrete transparent boundary conditions for the Schrödinger equation: fast calculation, approximation, and stability
• Far Field Boundary Conditions for Black--Scholes Equations
• Quadratic Convergence for Valuing American Options Using a Penalty Method
• The numerical solution of second-order boundary value problems on nonuniform meshes
• A Fast Numerical Method for the Black--Scholes Equation of American Options
• Finite Element Error Estimates for a Nonlocal Problem in American Option Valuation
• Tools for computational finance.

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