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

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

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Article number104345
JournalJournal of Economic Dynamics and Control
Volume137
DOIs
StatePublished - Apr 2022

Keywords

  • Cherny-Shiryaev-Yor invariance principle
  • Hedging transaction cost
  • Jarrow-Rudd binomial option pricing
  • Skew random walk

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