An Accurate Numerical Integrator for the Solution of Black Scholes Financial Model Equation

Abstract

In this paper the Black Scholes differential equation is transformed into a parabolic heat equation by appropriate change in variables. The transformed equation is semi-discretized by the Method of Lines (MOL). The evolving system of ordinary differential equations (ODEs) is integrated numerically by an L-stable trapezoidal-like integrator. Results show accuracy of relative maximum error of order 10 −10 .

Numerical analysis of the European and American options with the SPH method

“…Several numerical studies have been done to predict the European/American options. In most cases, the numerical schemes used are based on the finite difference method: (Acevedo and Lelièvre, 2018;Akpan and Fatokun, 2015;Anwar and Andallah, 2018;Company et al, 2009;Dilloo and Tangman, 2017;Khodayari and Ranjbar, 2018;Kiyoumarsi, 2018;Koleva and Vulkov, 2016;Matus et al, 2017;Rao and Manisha, 2018;Vahdati et al, 2018;Yousuf, 2018;Phaochoo et al, 2016;Zhang et al, 2016).…”