Displaying similar documents to “Convergence of a high-order compact finite difference scheme for a nonlinear Black–Scholes equation”

Convergence of a high-order compact finite difference scheme for a nonlinear Black–Scholes equation

Bertram Düring, Michel Fournié, Ansgar Jüngel (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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A high-order compact finite difference scheme for a fully nonlinear parabolic differential equation is analyzed. The equation arises in the modeling of option prices in financial markets with transaction costs. It is shown that the finite difference solution converges locally uniformly to the unique viscosity solution of the continuous equation. The proof is based on a careful study of the discretization matrices and on an abstract convergence result due to Barles and Souganides. ...

Nonstandard Finite Difference Schemes with Application to Finance: Option Pricing

Milev, Mariyan, Tagliani, Aldo (2010)

Serdica Mathematical Journal

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2000 Mathematics Subject Classification: 65M06, 65M12. The paper is devoted to pricing options characterized by discontinuities in the initial conditions of the respective Black-Scholes partial differential equation. Finite difference schemes are examined to highlight how discontinuities can generate numerical drawbacks such as spurious oscillations. We analyze the drawbacks of the Crank-Nicolson scheme that is most frequently used numerical method in Finance because of its...

Consistent stable difference schemes for nonlinear Black-Scholes equations modelling option pricing with transaction costs

Rafael Company, Lucas Jódar, José-Ramón Pintos (2009)

ESAIM: Mathematical Modelling and Numerical Analysis

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This paper deals with the numerical solution of nonlinear Black-Scholes equation modeling European vanilla call option pricing under transaction costs. Using an explicit finite difference scheme consistent with the partial differential equation valuation problem, a sufficient condition for the stability of the solution is given in terms of the stepsize discretization variables and the parameter measuring the transaction costs. This stability condition is linked to some properties of...