Market complete option valuation using a Jarrow-Rudd pricing tree with skewness and kurtosis

• DOI: 10.1016/j.jedc.2022.104345
• Publication Date: 2022-02-26T07:27:42Z
• Authors: Yuan Hu; W. Brent Lindquist; Svetlozar T. Rachev; Abootaleb Shirvani; Frank J. Fabozzi
• Keywords: Kurtosis; Trinomial tree

25 pages, 12 figures<br/>Applying the Cherny-Shiryaev-Yor invariance principle, we introduce a generalized Jarrow-Rudd (GJR) option pricing model with uncertainty driven by a skew random walk. The GJR pricing tree exhibits skewness and kurtosis in both the natural and risk-neutral world. We construct implied surfaces for the parameters determining the GJR tree. Motivated by Merton's pricing tree incorporating transaction costs, we extend the GJR pricing model to include a hedging cost. We demonstrate ways to fit the GJR pricing model to a market driver that influences the price dynamics of the underlying asset. We supplement our findings with numerical examples.<br/>