The analytical solution for the Black-Scholes equation with two assets in the Liouville-Caputo fractional derivative sense

DOI10.3390/math6080129zbMath1418.91536OpenAlexW2884159111WikidataQ129486268 ScholiaQ129486268MaRDI QIDQ1634384

Wannika Sawangtong, Benchawan Wiwattanapataphee, Panumart Sawangtong, Kamonchat Trachoo

Publication date: 18 December 2018

Published in: Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3390/math6080129

zbMATH Keywords

fractional derivativesBlack-Scholes modelgeneralized Mittag-Leffer functionLaplace transform homotopy perturbation method

Mathematics Subject Classification ID

Fractional derivatives and integrals (26A33) Derivative securities (option pricing, hedging, etc.) (91G20) Laplace transform (44A10)

Related Items (7)

Solving Black-Scholes equations using fractional generalized homotopy analysis method ⋮ Novel approaches for getting the solution of the fractional Black-Scholes equation described by Mittag-Leffler fractional derivative ⋮ An alternative method for analytical solutions of two-dimensional Black-Scholes-Merton equation ⋮ Linearly autonomous symmetries of a fractional Guéant-Pu model ⋮ Improved numerical solution of multi-asset option pricing problem: a localized RBF-FD approach ⋮ Black-Scholes option pricing equations described by the Caputo generalized fractional derivative ⋮ Meshless RBFs method for numerical solutions of two-dimensional high order fractional Sobolev equations

Cites Work

• The Pricing of Options and Corporate Liabilities
• Bernstein's inequalities and their extensions for getting the Black-Scholes option pricing formula
• A practical finite difference method for the three-dimensional Black-Scholes equation
• A radial basis function partition of unity collocation method for convection-diffusion equations arising in financial applications
• A robust and accurate finite difference method for a generalized Black-Scholes equation
• A robust finite difference scheme for pricing American put options with singularity-separating method
• Some notes on using the homotopy perturbation method for solving time-dependent differential equations
• Derivation and solutions of some fractional Black-Scholes equations in coarse-grained space and time. Application to Merton's optimal portfolio
• An upwind approach for an American and European option pricing model
• Option pricing beyond Black-Scholes based on double-fractional diffusion
• Optimal selection of local approximants in RBF-PU interpolation
• \textsc{OpenCL} based parallel algorithm for RBF-PUM interpolation
• Homotopy perturbation method for bifurcation of nonlinear problems
• On the use of boundary conditions for variational formulations arising in financial mathematics.
• Comparison of Black-Scholes formula with fractional Black-Scholes formula in the foreign exchange option market with changing volatility
• Homotopy perturbation technique
• Radial basis function partition of unity methods for pricing vanilla basket options
• Numerical solution of the time fractional Black-Scholes model governing European options
• Solution of the fractional Black-Scholes option pricing model by finite difference method
• Mellin transform method for European option pricing with Hull-White stochastic interest rate
• A single quenching point for a fractional heat equation based on the Riemann-Liouville fractional derivative with a nonlinear concentrate source
• An upwind finite difference method for a nonlinear Black-Scholes equation governing European option valuation under transaction costs
• A note on Wick products and the fractional Black-Scholes model
• A closed-form approximation for the fractional Black-Scholes model with transaction costs
• Brownian Motion in the Stock Market
• Option pricing: A simplified approach

This page was built for publication: The analytical solution for the Black-Scholes equation with two assets in the Liouville-Caputo fractional derivative sense