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Option Pricing Using a Skew Random Walk Binary Tree

Author

Listed:
  • Yuan Hu

    (Independent Researcher, 1620 E. Jefferson St. 312, Rockville, MD 20852, USA)

  • W. Brent Lindquist

    (Department of Mathematics & Statistics, Texas Tech University, Lubbock, TX 79406-1042, USA)

  • Svetlozar T. Rachev

    (Department of Mathematics & Statistics, Texas Tech University, Lubbock, TX 79406-1042, USA)

  • Frank J. Fabozzi

    (Carey Business School, Johns Hopkins University, Baltimore, MD 21202, USA)

Abstract

We develop a binary tree pricing model with underlying asset price dynamics following Itô–McKean skew Brownian motion. Our work was motivated by the Corns–Satchell, continuous-time, option pricing model. However, the Corns–Satchell market model is incomplete, while our discrete-time market model is defined in the natural world, extended to the risk-neutral world under the no-arbitrage condition where derivatives are priced under uniquely determined risk-neutral probabilities, and is complete. The skewness introduced in the natural world is preserved in the risk-neutral world. Furthermore, we show that the model preserves skewness under the continuous-time limit. We provide empirical applications of our model to the valuation of European put and call options on exchange-traded funds tracking the S&P Global 1200 index.

Suggested Citation

  • Yuan Hu & W. Brent Lindquist & Svetlozar T. Rachev & Frank J. Fabozzi, 2024. "Option Pricing Using a Skew Random Walk Binary Tree," JRFM, MDPI, vol. 17(4), pages 1-29, March.
    • Handle: RePEc:gam:jjrfmx:v:17:y:2024:i:4:p:138-:d:1364755
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    References listed on IDEAS

    as
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    2. W. Brent Lindquist & Svetlozar T. Rachev, 2025. "Alternatives to classical option pricing," Annals of Operations Research, Springer, vol. 346(1), pages 489-509, March.

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