Laplace transform and finite difference methods for the Black-Scholes equation

DOI10.1016/j.amc.2013.07.011zbMath1329.91143OpenAlexW2084759080MaRDI QIDQ902554

Aldo Tagliani, Mariyan Milev

Publication date: 18 January 2016

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

Full work available at URL: https://doi.org/10.1016/j.amc.2013.07.011

zbMATH Keywords

Laplace transformfinite difference scheme\(M\)-matrixBlack-Scholes equationcompletely monotonic functionpositivity-preservingpost-widder formula

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) Laplace transform (44A10)

Related Items (12)

Integral transform approach to mimetic discrete calculus ⋮ Unnamed Item ⋮ A new finite difference method for pricing and hedging fixed income derivatives: comparative analysis and the case of an Asian option ⋮ A numerical method for pricing discrete double barrier option by Lagrange interpolation on Jacobi nodes ⋮ Accurate and efficient computations of the Greeks for options near expiry using the Black-Scholes equations ⋮ Numerical method of pricing discretely monitored barrier option ⋮ Evolving generation and fast algorithms of slantlet transform and slantlet-Walsh transform ⋮ Semi-numerical solution to a fractal telegraphic dual-porosity fluid flow model ⋮ An RBF-FD sparse scheme to simulate high-dimensional Black-Scholes partial differential equations ⋮ Robust numerical algorithm to the European option with illiquid markets ⋮ A numerical method to price discrete double Barrier options under a constant elasticity of variance model with jump diffusion ⋮ A meshless method for Asian style options pricing under the Merton jump-diffusion model

Uses Software

• Algorithm 368

Cites Work

• The Pricing of Options and Corporate Liabilities
• A distributed algorithm for European options with nonlinear volatility
• Numerical methods for Laplace transform inversion
• Far Field Boundary Conditions for Black--Scholes Equations
• An Inversion Technique for the Laplace Transform
• Completely monotonic functions
• Eigenvalues of complex tridiagonal matrices
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