Option Pricing Using a Skew Random Walk Binary Tree

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.

Description

© 2024 by the authors. cc-by

Keywords

binary pricing tree, complete markets, option pricing, skew Brownian motion

Citation

Hu, Y., Lindquist, W.B., Rachev, S.T., & Fabozzi, F.J.. 2024. Option Pricing Using a Skew Random Walk Binary Tree. Journal of Risk and Financial Management, 17(4). https://doi.org/10.3390/jrfm17040138

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