Asymptotic expansion of solutions to the Black-Scholes equation arising from American option pricing near the expiry

DOI10.1016/j.cam.2016.06.033zbMath1352.91034OpenAlexW2462562760MaRDI QIDQ730511

Mehdi Dehghan, Ali Foroush Bastani, Seyed-Mohammad-Mahdi Kazemi

Publication date: 28 December 2016

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

Full work available at URL: https://doi.org/10.1016/j.cam.2016.06.033

zbMATH Keywords

transparent boundary conditionsBlack-Scholes equationfree boundary value problemAmerican call optionPoincaré asymptotic expansionrepeated integral of the complementary error functions

Mathematics Subject Classification ID

Numerical methods (including Monte Carlo methods) (91G60) Error bounds for boundary value problems involving PDEs (65N15) Stopping times; optimal stopping problems; gambling theory (60G40) Derivative securities (option pricing, hedging, etc.) (91G20) Free boundary problems for PDEs (35R35) Asymptotic expansions of solutions to ordinary differential equations (34E05)

Related Items (12)

An upwind local radial basis functions-differential quadrature (RBF-DQ) method with proper orthogonal decomposition (POD) approach for solving compressible Euler equation ⋮ A trustable shape parameter in the kernel-based collocation method with application to pricing financial options ⋮ On a new family of radial basis functions: mathematical analysis and applications to option pricing ⋮ On the numerical solution of time fractional Black-Scholes equation ⋮ A reduced-order model based on cubic B-spline basis function and SSP Runge-Kutta procedure to investigate option pricing under jump-diffusion models ⋮ An explicit spectral collocation method for the linearized Korteweg-de Vries equation on unbounded domain ⋮ Fast and accurate calculation of American option prices ⋮ The dynamics of a spatial economic model with bounded population growth ⋮ A new method for evaluating options based on multiquadric RBF-FD method ⋮ An Efficient Numerical Method for the Valuation of American Better-of Options Based on the Front-Fixing Transform and the Far Field Truncation ⋮ Legendre wavelet based numerical solution of variable latent heat moving boundary problem ⋮ Boundary shape function iterative method for nonlinear second-order boundary value problems with nonlinear boundary conditions

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• An artificial boundary method for the Hull-White model of American interest rate derivatives
• On the solution of the non-local parabolic partial differential equations via radial basis functions
• Mathematical models of financial derivatives
• A fast high-order finite difference algorithm for pricing American options
• Numerical solution of problems on unbounded domains. A review
• Asymptotic analysis of American call options
• Efficient techniques for the second-order parabolic equation subject to nonlocal specifications
• Far Field Boundary Conditions for Black--Scholes Equations
• CRITICAL STOCK PRICE NEAR EXPIRATION
• An Artificial Boundary Method for American Option Pricing under the CEV Model
• A FAST, STABLE AND ACCURATE NUMERICAL METHOD FOR THE BLACK–SCHOLES EQUATION OF AMERICAN OPTIONS
• A Mathematical Analysis of the Optimal Exercise Boundary for American Put Options
• Evaluation of Repeated Integrals of the Coerror Function
• A Fast Numerical Method for the Black--Scholes Equation of American Options
• Finite Element Error Estimates for a Nonlocal Problem in American Option Valuation
• Optimal exercise boundary for an American put option
• Nine Ways to Implement the Binomial Method for Option Valuation in MATLAB
• American options on assets with dividends near expiry
• Asymptotic analysis of the American call option with dividends
• Artificial Boundary Method
• PRICING AND HEDGING AMERICAN OPTIONS ANALYTICALLY: A PERTURBATION METHOD

This page was built for publication: Asymptotic expansion of solutions to the Black-Scholes equation arising from American option pricing near the expiry