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A novel analytical technique for the solution of time-fractional Ivancevic option pricing model

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  • Jena, Rajarama Mohan
  • Chakraverty, Snehashish
  • Baleanu, Dumitru

Abstract

The Ivancevic option pricing model is an alternative of the standard Black–Scholes pricing equation, which signifies a controlled Brownian motion related to the nonlinear Schrodinger equation. Even though many researchers have studied the applicability and practicality of this model, but the analytical approach of this model is rarely found in the literature. In this paper, a novel semi-analytical technique called fractional reduced differential transform method has been applied to solve the Schrodinger type option pricing model, which is characterized by the time-fractional derivative. Two problems are explained to validate and prove the effectiveness of the proposed technique. Obtained results are compared with the solution of other existing methods for a particular case. This comparison shows that the attained results are in good agreement with the existing solutions.

Suggested Citation

  • Jena, Rajarama Mohan & Chakraverty, Snehashish & Baleanu, Dumitru, 2020. "A novel analytical technique for the solution of time-fractional Ivancevic option pricing model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 550(C).
    • Handle: RePEc:eee:phsmap:v:550:y:2020:i:c:s0378437120301436
    DOI: 10.1016/j.physa.2020.124380
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    References listed on IDEAS

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    1. Contreras, Mauricio & Pellicer, Rely & Villena, Marcelo & Ruiz, Aaron, 2010. "A quantum model of option pricing: When Black–Scholes meets Schrödinger and its semi-classical limit," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(23), pages 5447-5459.
    2. R. Cont, 2001. "Empirical properties of asset returns: stylized facts and statistical issues," Quantitative Finance, Taylor & Francis Journals, vol. 1(2), pages 223-236.
    3. 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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    1. Jena, Rajarama Mohan & Chakraverty, Snehashish & Jena, Subrat Kumar, 2020. "Analysis of the dynamics of phytoplankton nutrient and whooping cough models with nonsingular kernel arising in the biological system," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).

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