Analysis of a Hybrid Finite Difference Scheme for the Black-Scholes Equation Governing Option Pricing
نویسندگان
چکیده
Abstract. In this paper we present a hybrid finite difference scheme on a piecewise uniform mesh for a class of Black-Scholes equations governing option pricing which is path-dependent. In spatial discretization a hybrid finite difference scheme combining a central difference method with an upwind difference method on a piecewise uniform mesh is used. For the time discretization, we use an implicit difference method on a uniform mesh. Applying the discrete maximum principle and barrier function technique we prove that our scheme is second-order convergent in space for the arbitrary volatility and the arbitrary asset price. Numerical results support the theoretical results.
منابع مشابه
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.
متن کاملA 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.
متن کاملA Second-order Finite Difference Scheme for a Type of Black-Scholes Equation
In this paper we consider a backward parabolic partial differential equation, called the Black-Scholes equation, governing American and European option pricing. We present a numerical method combining the Crank-Nicolson method in the time discretization with a hybrid finite difference scheme on a piecewise uniform mesh in the spatial discretization. The difference scheme is stable for the arbit...
متن کاملA new approach to using the cubic B-spline functions to solve the Black-Scholes equation
Nowadays, options are common financial derivatives. For this reason, by increase of applications for these financial derivatives, the problem of options pricing is one of the most important economic issues. With the development of stochastic models, the need for randomly computational methods caused the generation of a new field called financial engineering. In the financial engineering the pre...
متن کاملEuropean option pricing of fractional Black-Scholes model with new Lagrange multipliers
In this paper, a new identification of the Lagrange multipliers by means of the Sumudu transform, is employed to btain a quick and accurate solution to the fractional Black-Scholes equation with the initial condition for a European option pricing problem. Undoubtedly this model is the most well known model for pricing financial derivatives. The fractional derivatives is described in Caputo sen...
متن کامل