Application of analytical techniques to solve the Black-Scholes model, a theoretically estimate of the price of European style options involving three assets

Tayyab Zamir , Farooq Ahmed Shah , Ehsan ul Haq

Abstract

In response to the growing importance of multi-asset option pricing, this study explores the three-asset Black-Scholes model and its practical applications in actuarial science. The governing partial differential equation presents computational challenges, which are addressed using two analytical iterative techniques—the variational iteration method and the variation of parameters method. The incorporation of the Lagrange multiplier reduces complexity and enhances convergence in the solution process. Numerical results are presented in graphical and tabular form using Maple software to facilitate interpretation and demonstrate the effectiveness of the proposed methods. The findings indicate that both techniques yield accurate and computationally efficient solutions. Overall, this work provides valuable insights into multi-asset option pricing and offers methodological tools that can be extended to other complex mathematical models. The methods and tools used in this study can be applied to other mathematical models and fields, thereby advancing the development of more accurate and efficient models.

Key Words

Black Scholes model; option pricing model; variational iteration method; variational parameter method and Lagrange multiplier

Address

Tayyab Zamir, Farooq Ahmed Shah — Department of Mathematics, COMSATS University Islamabad, Attock Campus, Pakistan
Ehsan ul Haq — Department of Mathematics, University of Wah, Pakistan

PDF Viewer

Preview is limited to the first 3 pages. Sign in to access the full PDF.

← Back to Volume 37, No. 4