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Derivative pricing with non-linear Fokker–Planck dynamics

Author

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  • Michael, Fredrick
  • Johnson, M.D.

Abstract

We examine how the Black–Scholes derivative pricing formula is modified when the underlying security obeys non-extensive statistics and Fokker–Planck dynamics. An unusual feature of such securities is that the volatility in the underlying Ito–Langevin equation depends implicitly on the actual market rate of return. This complicates most approaches to valuation. Here we show that progress is possible using variations of the Cox–Ross valuation technique.

Suggested Citation

  • Michael, Fredrick & Johnson, M.D., 2003. "Derivative pricing with non-linear Fokker–Planck dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 324(1), pages 359-365.
    • Handle: RePEc:eee:phsmap:v:324:y:2003:i:1:p:359-365
    DOI: 10.1016/S0378-4371(02)01906-4
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    Cited by:

    1. Chargoy-Corona, Jesús & Ibarra-Valdez, Carlos, 2006. "A note on Black–Scholes implied volatility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 370(2), pages 681-688.
    2. Arias-Calluari, Karina & Najafi, Morteza. N. & Harré, Michael S. & Tang, Yaoyue & Alonso-Marroquin, Fernando, 2022. "Testing stationarity of the detrended price return in stock markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 587(C).
    3. Devi, Sandhya, 2021. "Asymmetric Tsallis distributions for modeling financial market dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 578(C).

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