Abstract
Since financial engineering problems are of great importance in the academic community, effective methods are still needed to analyze these models. Therefore, this article focuses mainly on capturing the discrete behavior of linear and nonlinear Black–Scholes European option pricing models. To achieve this, this article presents a combined method; a sixth order finite difference (FD6) scheme in space and a third–order strong stability preserving Runge–Kutta (SSPRK3) over time. The computed results are compared with available literature and the exact solution. The computed results revealed that the current method seems to be quite strong both quantitatively and qualitatively with minimal computational effort. Therefore, this method appears to be a very reliable alternative and flexible to implement in solving the problem while preserving the physical properties of such realistic processes.
Highlights
IntroductionIn the last few decades, the corporations looked for important tools in terms of financial securities
In the last few decades, the corporations looked for important tools in terms of financial securities.As part of the financial securities, options are mainly used to assure assets in order to cover the risks generated in the stock prices changes [1]
To properly understand what alternatives we have for these options, Lesmana and Wang [2] stated that there are two main types of options: European options can only be exercised on a given date and American options can be exercised on or before the expiry date
Summary
In the last few decades, the corporations looked for important tools in terms of financial securities. In the case of a nonlinear parabolic partial differential equation that governs the European option pricing in transaction costs, it is worth pointing out the contribution to Lesmana and Wang [2] who proposed an upwind difference scheme for spatial discretization. In this article, a sixth order finite difference scheme (FD6) in space and a third-order strong stability preserving Runge–Kutta (SSP-RK3) in time have been combined to obtain effective numerical solutions of the European put option problem that has an exact closed-form solution. This choice provides a direct and accurate estimation of approximation error.
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