Market Complete Option Valuation using a Jarrow-Rudd Pricing Tree with Skewness and Kurtosis

Yuan Hu, Abootaleb Shirvani, W. Brent Lindquist, Frank J. Fabozzi and Svetlozar T. Rachev

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Abstract: 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.

Date: 2021-06
New Economics Papers: this item is included in nep-rmg
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