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A Metaheuristic Approach to Optimize European Call Function with Boundary Conditions

Author

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  • Khan Najeeb Alam

    (Department of Mathematics, University of Karachi, Karachi75270, Pakistan)

  • Razzaq Oyoon Abdul

    (Department of Humanities & Natural Sciences, Bahria University, Karachi75260, Pakistan)

  • Hameed Tooba

    (Department of Mathematics, University of Karachi, Karachi75270, Pakistan)

Abstract

The purpose of this paper is to investigate the pricing European call option valuation problems under the exercise price, maturity, risk-free interest rate, and the volatility function. An advance methodology, Chebyshev simulated annealing neural network (ChSANN), is enforced for the Black-Scholes (B-S) model with boundary conditions. Our scheme is stable and easy to implement on B-S equation, for arbitrary volatility and arbitrary interest rate values. Also, the comparative results demonstrate that the attained approximate solutions are converging towards the exact solution. The graphical results show that the increasing flow of the European call option as the exponential increase takes place in assets. The presented algorithm can be further applied to other financial models with certain boundary conditions. The algorithm of the method shows that the approach can also be easily employed on time-fractional B-S equation.

Suggested Citation

  • Khan Najeeb Alam & Razzaq Oyoon Abdul & Hameed Tooba, 2018. "A Metaheuristic Approach to Optimize European Call Function with Boundary Conditions," Journal of Systems Science and Information, De Gruyter, vol. 6(3), pages 260-268, June.
    • Handle: RePEc:bpj:jossai:v:6:y:2018:i:3:p:260-268:n:5
    DOI: 10.21078/JSSI-2018-260-09
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    References listed on IDEAS

    as
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    4. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
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