SPECTRALLY ACCURATE OPTION PRICING UNDER THE TIME-FRACTIONAL BLACK–SCHOLES MODEL

DOI10.1017/S1446181121000286zbMath1484.91520OpenAlexW3195877470MaRDI QIDQ5158755

Désiré Yannick Tangman, Geraldine Tour, Nawdha Thakoor

Publication date: 26 October 2021

Published in: The ANZIAM Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s1446181121000286

zbMATH Keywords

option pricingtime-fractional Black-Scholes equationspectral element discretization

Mathematics Subject Classification ID

Numerical methods (including Monte Carlo methods) (91G60) Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Extrapolation to the limit, deferred corrections (65B05) Derivative securities (option pricing, hedging, etc.) (91G20) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) PDEs in connection with game theory, economics, social and behavioral sciences (35Q91)

Related Items (2)

High-order compact finite difference schemes for the time-fractional Black-Scholes model governing European options ⋮ A spectral collocation method based on fractional Pell functions for solving time-fractional Black-Scholes option pricing model

Cites Work

• Unnamed Item
• Unnamed Item
• The Pricing of Options and Corporate Liabilities
• Spectral and pseudospectral approximations for the time fractional diffusion equation on an unbounded domain
• Higher order numerical methods for solving fractional differential equations
• A predictor-corrector approach for pricing American options under the finite moment log-stable model
• Derivation and solutions of some fractional Black-Scholes equations in coarse-grained space and time. Application to Merton's optimal portfolio
• Numerical solution of fractional order differential equations by extrapolation
• Numerically pricing double barrier options in a time-fractional Black-Scholes model
• Numerical solution of time-fractional Black-Scholes equation
• A higher order numerical method for time fractional partial differential equations with nonsmooth data
• A 2nd-order ADI finite difference method for a 2D fractional Black-Scholes equation governing European two asset option pricing
• Numerical approximation of a time-fractional Black-Scholes equation
• A fast preconditioned iterative method for two-dimensional options pricing under fractional differential models
• Quintic B-spline collocation approach for solving generalized Black-Scholes equation governing option pricing
• Analytically pricing double barrier options based on a time-fractional Black-Scholes equation
• Numerical solution of the time fractional Black-Scholes model governing European options
• Fast numerical simulation of a new time-space fractional option pricing model governing European call option
• Solution of the fractional Black-Scholes option pricing model by finite difference method
• On the solution of two-dimensional fractional Black-Scholes equation for European put option
• An adaptive moving mesh method for a time-fractional Black-Scholes equation
• A sixth order numerical method and its convergence for generalized Black-Scholes PDE
• A fourth order numerical method based on B-spline functions for pricing Asian options
• A new operator splitting method for American options under fractional Black-Scholes models
• A high accuracy numerical method and its convergence for time-fractional Black-Scholes equation governing European options
• Numerical analysis of time fractional Black-Scholes European option pricing model arising in financial market
• Finite difference/spectral approximations for the distributed order time fractional reaction-diffusion equation on an unbounded domain
• Finite difference/spectral approximations for the time-fractional diffusion equation
• Numerical models for differential problems. Translated from the 5th Italian edition by Silvia Quarteroni
• An analysis of the L1 scheme for the subdiffusion equation with nonsmooth data
• Numerical Solutions of Fractional Differential Equations by Extrapolation
• Spectral Methods
• Finite difference/spectral approximations for the fractional cable equation
• Analytically pricing European-style options under the modified Black-Scholes equation with a spatial-fractional derivative
• Pricing Options in Jump-Diffusion Models: An Extrapolation Approach
• An Analysis of the Modified L1 Scheme for Time-Fractional Partial Differential Equations with Nonsmooth Data

This page was built for publication: SPECTRALLY ACCURATE OPTION PRICING UNDER THE TIME-FRACTIONAL BLACK–SCHOLES MODEL