Option Pricing Using a Skew Random Walk Binary Tree

Yuan Hu, W. Brent Lindquist (), Svetlozar T. Rachev and Frank J. Fabozzi
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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

JRFM, 2024, vol. 17, issue 4, 1-29

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.

Keywords: option pricing; binary pricing tree; skew Brownian motion; complete markets (search for similar items in EconPapers)
JEL-codes: C E F2 F3 G (search for similar items in EconPapers)
Date: 2024
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