The purpose of this paper was to investigate the dynamics of the option pricing in the market
through the two-dimensional time fractional-order Black–Scholes equation for a European …

It is well known that the Black-Scholes model is used to establish the behavior of the option
pricing in the financial market. In this paper, we propose the modified version of Black …

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 …

Proper pricing of options in the financial derivative market is crucial. For many options, it is
often impossible to obtain analytical solutions to the Black–Scholes (BS) equation. Hence an …

In this paper, we use a numerical method for solving the nonlinear Black–Scholes partial
differential equation of the European option under transaction costs, which is based on the …

Dividend paying European stock options are modeled using a time-fractional Black–Scholes
(tfBS) partial differential equation (PDE). The underlying fractional stochastic dynamics …

The fractional form of the classical diffusion equation embodies the super-diffusive and sub-
diffusive characteristics of any flow, depending on the fractional order. This study aims to …

In this paper we develop a numerical approach to a fractional-order differential Linear
Complementarity Problem (LCP) arising in pricing European and American options under a …

After the discovery of the fractal structures of financial markets, enormous effort has been
dedicated to finding accurate and stable numerical schemes to solve fractional Black …

A fast preconditioned penalty method is developed for a system of parabolic linear
complementarity problems (LCPs) involving tempered fractional order partial derivatives …