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Option Pricing Incorporating Factor Dynamics in Complete Markets

Author

Listed:
  • Yuan Hu

    (Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX 79409-1042, USA)

  • Abootaleb Shirvani

    (Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX 79409-1042, USA)

  • W. Brent Lindquist

    (Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX 79409-1042, USA)

  • Frank J. Fabozzi

    (Finance Department, EDHEC Business School, 393/400 Promenade des Anglais-BP3116, CEDEX 3, 06202 Nice, France)

  • Svetlozar T. Rachev

    (Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX 79409-1042, USA)

Abstract

Using the Donsker–Prokhorov invariance principle, we extend the Kim–Stoyanov–Rachev–Fabozzi option pricing model to allow for variably-spaced trading instances, an important consideration for short-sellers of options. Applying the Cherny–Shiryaev–Yor invariance principles, we formulate a new binomial path-dependent pricing model for discrete- and continuous-time complete markets where the stock price dynamics depends on the log-return dynamics of a market influencing factor. In the discrete case, we extend the results of this new approach to a financial market with informed traders employing a statistical arbitrage strategy involving trading of forward contracts. Our findings are illustrated with numerical examples employing US financial market data. Our work provides further support for the conclusion that any option pricing model must preserve valuable information on the instantaneous mean log-return, the probability of the stock’s upturn movement (per trading interval), and other market microstructure features.

Suggested Citation

  • Yuan Hu & Abootaleb Shirvani & W. Brent Lindquist & Frank J. Fabozzi & Svetlozar T. Rachev, 2020. "Option Pricing Incorporating Factor Dynamics in Complete Markets," JRFM, MDPI, vol. 13(12), pages 1-33, December.
    • Handle: RePEc:gam:jjrfmx:v:13:y:2020:i:12:p:321-:d:462729
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    Cited by:

    1. Yuan Hu & Abootaleb Shirvani & W. Brent Lindquist & Frank J. Fabozzi & Svetlozar T. Rachev, 2021. "Market Complete Option Valuation using a Jarrow-Rudd Pricing Tree with Skewness and Kurtosis," Papers 2106.09128, arXiv.org.
    2. Hu, Yuan & Lindquist, W. Brent & Rachev, Svetlozar T. & Shirvani, Abootaleb & Fabozzi, Frank J., 2022. "Market complete option valuation using a Jarrow-Rudd pricing tree with skewness and kurtosis," Journal of Economic Dynamics and Control, Elsevier, vol. 137(C).
    3. Davide Lauria & W. Brent Lindquist & Svetlozar T. Rachev & Yuan Hu, 2023. "Unifying Market Microstructure and Dynamic Asset Pricing," Papers 2304.02356, arXiv.org, revised Feb 2024.

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