A practical finite difference method for the three-dimensional Black-Scholes equation

DOI10.1016/j.ejor.2015.12.012zbMath1346.91258OpenAlexW2196471905MaRDI QIDQ322864

Seunggyu Lee, Taekkeun Kim, Minhyun Yoo, Yongho Choi, Darae Jeong, Jaehyun Jo, Hyeongseok Hwang, Junseok Kim

Publication date: 7 October 2016

Published in: European Journal of Operational Research (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.ejor.2015.12.012

zbMATH Keywords

option pricingoperator splitting methodBlack-Scholes partial differential equationequity-linked securitiesnon-uniform grid

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) PDEs in connection with game theory, economics, social and behavioral sciences (35Q91)

Related Items (9)

The analytical solution for the Black-Scholes equation with two assets in the Liouville-Caputo fractional derivative sense ⋮ An accurate and stable numerical method for option hedge parameters ⋮ An alternative method for analytical solutions of two-dimensional Black-Scholes-Merton equation ⋮ An operator splitting method for multi-asset options with the Feynman-Kac formula ⋮ Unnamed Item ⋮ Optimal non-uniform finite difference grids for the Black-Scholes equations ⋮ Equity-linked security pricing and greeks at arbitrary intermediate times using Brownian bridge ⋮ CDS pricing with fractional Hawkes processes ⋮ Practical finite difference method for solving multi-dimensional Black-Scholes model in fractal market

Uses Software

• Mathematica

Cites Work

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• The Pricing of Options and Corporate Liabilities
• Robust option pricing
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• On multigrid for anisotropic equations and variational inequalities ``pricing multi-dimensional European and American options
• A comparison study of ADI and operator splitting methods on option pricing models
• High-order computational methods for option valuation under multifactor models
• Optimizing bounds on security prices in incomplete markets. Does stochastic volatility specification matter?
• Hedging conditional value at risk with options
• Positive numerical solution for a nonarbitrage liquidity model using nonstandard finite difference schemes
• Some mathematical results in the pricing of American options
• A Fast Numerical Method for the Black--Scholes Equation of American Options
• Option pricing and Greeks via a moving least square meshfree method
• AN ACCURATE AND EFFICIENT NUMERICAL METHOD FOR BLACK-SCHOLES EQUATIONS

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