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A model for stocks dynamics based on a non-Gaussian path integral

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  • Paolinelli, Giovanni
  • Arioli, Gianni

Abstract

We introduce a model for the dynamics of stock prices based on a non quadratic path integral. The model is a generalization of Ilinski’s path integral model, more precisely we choose a different action, which can be tuned to different time scales. The result is a model with a very small number of parameters that provides very good fits of some stock prices and indices fluctuations.

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  • Paolinelli, Giovanni & Arioli, Gianni, 2019. "A model for stocks dynamics based on a non-Gaussian path integral," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 517(C), pages 499-514.
    • Handle: RePEc:eee:phsmap:v:517:y:2019:i:c:p:499-514
    DOI: 10.1016/j.physa.2018.11.044
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    References listed on IDEAS

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    1. Adrian Dragulescu & Victor Yakovenko, 2002. "Probability distribution of returns in the Heston model with stochastic volatility," Quantitative Finance, Taylor & Francis Journals, vol. 2(6), pages 443-453.
    2. Paolinelli, Giovanni & Arioli, Gianni, 2018. "A path integral based model for stocks and order dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 510(C), pages 387-399.
    3. Devreese, J.P.A. & Lemmens, D. & Tempere, J., 2010. "Path integral approach to Asian options in the Black–Scholes model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(4), pages 780-788.
    4. Kleinert, Hagen, 2002. "Option pricing from path integral for non-Gaussian fluctuations. Natural martingale and application to truncated Lèvy distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 312(1), pages 217-242.
    5. Dupoyet, B. & Fiebig, H.R. & Musgrove, D.P., 2010. "Gauge invariant lattice quantum field theory: Implications for statistical properties of high frequency financial markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(1), pages 107-116.
    6. Giovanni Paolinelli & Gianni Arioli, 2018. "A path integral based model for stocks and order dynamics," Papers 1803.07904, arXiv.org.
    7. G. Bormetti & G. Montagna & N. Moreni & O. Nicrosini, 2006. "Pricing exotic options in a path integral approach," Quantitative Finance, Taylor & Francis Journals, vol. 6(1), pages 55-66.
    8. Kleinert, Hagen, 2002. "Stochastic calculus for assets with non-Gaussian price fluctuations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 311(3), pages 536-562.
    9. Bidarkota, Prasad V. & Dupoyet, Brice V., 2007. "The impact of fat tails on equilibrium rates of return and term premia," Journal of Economic Dynamics and Control, Elsevier, vol. 31(3), pages 887-905, March.
    10. Montagna, Guido & Nicrosini, Oreste & Moreni, Nicola, 2002. "A path integral way to option pricing," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 310(3), pages 450-466.
    11. Kleinert, Hagen, 2004. "Option pricing for non-Gaussian price fluctuations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 338(1), pages 151-159.
    12. Dupoyet, B. & Fiebig, H.R. & Musgrove, D.P., 2011. "Replicating financial market dynamics with a simple self-organized critical lattice model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(18), pages 3120-3135.
    13. G. Montagna & O. Nicrosini & N. Moreni, 2002. "A Path Integral Way to Option Pricing," Papers cond-mat/0202143, arXiv.org.
    14. Giovanni Paolinelli & Gianni Arioli, 2018. "A model for stocks dynamics based on a non-Gaussian path integral," Papers 1809.01342, arXiv.org, revised Oct 2018.
    15. Eleonora Bennati & Marco Rosa-Clot & Stefano Taddei, 1999. "A Path Integral Approach To Derivative Security Pricing I: Formalism And Analytical Results," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 2(04), pages 381-407.
    16. Marco Rosa-Clot & Stefano Taddei, 1999. "A Path Integral Approach to Derivative Security Pricing: II. Numerical Methods," Papers cond-mat/9901279, arXiv.org.
    17. Dupoyet, B. & Fiebig, H.R. & Musgrove, D.P., 2012. "Arbitrage-free self-organizing markets with GARCH properties: Generating them in the lab with a lattice model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(18), pages 4350-4363.
    18. Marco Rosa-Clot & Stefano Taddei, 1999. "A Path Integral Approach to Derivative Security Pricing: I. Formalism and Analytical Results," Papers cond-mat/9901277, arXiv.org.
    19. G. Bormetti & G. Montagna & N. Moreni & O. Nicrosini, 2004. "Pricing Exotic Options in a Path Integral Approach," Papers cond-mat/0407321, arXiv.org, revised May 2006.
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