  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.
