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

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. (c) 2022 Elsevier B.V. All rights reserved.