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Hamiltonian and potentials in derivative pricing models: exact results and lattice simulations

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  • Baaquie, Belal E.
  • Corianò, Claudio
  • Srikant, Marakani

Abstract

The pricing of options, warrants and other derivative securities is one of the great success of financial economics. These financial products can be modeled and simulated using quantum mechanical instruments based on a Hamiltonian formulation. We show here some applications of these methods for various potentials, which we have simulated via lattice Langevin and Monte Carlo algorithms, to the pricing of options. We focus on barrier or path dependent options, showing in some detail the computational strategies involved.

Suggested Citation

  • Baaquie, Belal E. & Corianò, Claudio & Srikant, Marakani, 2004. "Hamiltonian and potentials in derivative pricing models: exact results and lattice simulations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 334(3), pages 531-557.
    • Handle: RePEc:eee:phsmap:v:334:y:2004:i:3:p:531-557
    DOI: 10.1016/j.physa.2003.10.080
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    References listed on IDEAS

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    1. Linetsky, Vadim, 1998. "The Path Integral Approach to Financial Modeling and Options Pricing," Computational Economics, Springer;Society for Computational Economics, vol. 11(1-2), pages 129-163, April.
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    Cited by:

    1. Axel A. Araneda & Marcelo J. Villena, 2018. "Computing the CEV option pricing formula using the semiclassical approximation of path integral," Papers 1803.10376, arXiv.org.
    2. Chowdhury, Reaz & Mahdy, M.R.C. & Alam, Tanisha Nourin & Al Quaderi, Golam Dastegir & Arifur Rahman, M., 2020. "Predicting the stock price of frontier markets using machine learning and modified Black–Scholes Option pricing model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 555(C).
    3. Ivan Arraut & Alan Au & Alan Ching-biu Tse & Joao Alexandre Lobo Marques, 2019. "On the probability flow in the Stock market I: The Black-Scholes case," Papers 2001.00516, arXiv.org.
    4. Shi, Leilei, 2006. "Does security transaction volume–price behavior resemble a probability wave?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 366(C), pages 419-436.
    5. Haoran Zheng & Jing Bai, 2024. "Quantum Leap: A Price Leap Mechanism in Financial Markets," Mathematics, MDPI, vol. 12(2), pages 1-27, January.
    6. Bueno-Guerrero, Alberto, 2022. "A Quantum Mechanics for interest rate derivatives markets," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    7. Reaz Chowdhury & M. R. C. Mahdy & Tanisha Nourin Alam & Golam Dastegir Al Quaderi, 2018. "Predicting the Stock Price of Frontier Markets Using Modified Black-Scholes Option Pricing Model and Machine Learning," Papers 1812.10619, arXiv.org.
    8. Ivan Arraut & Alan Au & Alan Ching-biu Tse, 2020. "On the multiplicity of the martingale condition: Spontaneous symmetry breaking in Quantum Finance," Papers 2004.11270, arXiv.org.
    9. Ivan Arraut & João Alexandre Lobo Marques & Sergio Gomes, 2021. "The Probability Flow in the Stock Market and Spontaneous Symmetry Breaking in Quantum Finance," Mathematics, MDPI, vol. 9(21), pages 1-18, November.

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