Positive numerical splitting method for the Hull and White 2D Black-Scholes equation

Numerical Solutions for Fractional Black-Scholes Option Pricing Equation

In this article we have applied a numerical finite difference method to solve the Black-Scholes European and American option pricing both presented by fractional differential equations in time and asset.

A family of positive nonstandard numerical methods with application to Black-Scholes equation

Nonstandard finite difference schemes for the Black-Scholes partial differential equation preserving the positivity property are proposed. Computationally simple schemes are derived by using a nonlocal approximation in the reaction term of the Black-Scholes equation. Unlike the standard methods, the solutions of new proposed schemes are positive and free of the spurious oscillations.

Numerical Solution of Fractional Black Scholes Equation Based on Radial Basis Functions Method

Options pricing have an important role in risk control and risk management. Pricing discussion requires modelling process, solving methods and implementing the model by real data in a given market. In this paper we show a model for underlying asset based on fractional stochastic models which is a particular type of behavior of stochastic assets changing. In addition a numerical method based on ...

The use of iterative methods for solving Black-Scholes equation

A Fast, Stable and Accurate Numerical Method for the Black–scholes Equation of American Options

In this work we improve the algorithm of Han and Wu (SIAM J. Numer. Anal. 41 (2003), 2081–2095) for American Options with respect to stability, accuracy and order of computational effort. We derive an exact discrete artificial boundary condition (ABC) for the Crank–Nicolson scheme for solving the Black–Scholes equation for the valuation of American options. To ensure stability and to avoid any ...