Crank-Nicolson Analysis of Black-scholes Equation and Effects of Covariance Properties for Stock Market Prices
Mandah O.C
Department of Mathematics & Statistics, Captain Elechi Amadi Polytechnics, Port Harcourt, Nigeria.
Anthony, C.
Department of Mathematics & Statistics, Ignatius Ajuru University of Education, Port Harcourt, Nigeria.
Amadi, I.U
Department of Mathematics & Statistics, Captain Elechi Amadi Polytechnics, Port Harcourt, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
This paper analyzes the Black-Scholes partial differential equation for European option pricing using both analytical and numerical approaches. The Crank-Nicolson finite difference method is employed to obtain approximate solutions for call and put options, which are then compared with closed-form Black-Scholes prices. A covariance matrix analysis and quantile-quantile (QQ) normality test are conducted to evaluate the statistical properties of the approximate solutions. The results show a strong correlation between the analytical and numerical outcomes, supporting the robustness of the Crank-Nicolson approach in modeling option prices. These findings provide valuable insights for investors and enhance the reliability of numerical methods in financial decision-making.
Keywords: Black-Scholes, stock market, Crank-Nicolson, covariance, option traders