2023/03/29 by Hu, Yuan, Lindquist, W. Brent, Rachev, Svetlozar T. +1
#FOS: Economics and business #Mathematical Finance (q-fin.MF)
paper · doi:10.48550/arxiv.2303.17014
Motivated by the Corns-Satchell, continuous time, option pricing model, we develop a binary tree pricing model with underlying asset price dynamics following Itô-Mckean skew Brownian motion. While the Corns-Satchell market model is incomplete, 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 numerical applications of our model to the valuation of European put and call options on exchange-traded funds tracking the S&P Global 1200 index.