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

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

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.

Suggested Citation

  • Hu, Yuan & Lindquist, W. Brent & Rachev, Svetlozar T. & Shirvani, Abootaleb & Fabozzi, Frank J., 2022. "Market complete option valuation using a Jarrow-Rudd pricing tree with skewness and kurtosis," Journal of Economic Dynamics and Control, Elsevier, vol. 137(C).
    • Handle: RePEc:eee:dyncon:v:137:y:2022:i:c:s0165188922000501
    DOI: 10.1016/j.jedc.2022.104345
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    Cited by:

    1. W. Brent Lindquist & Svetlozar T. Rachev & Jagdish Gnawali & Frank J. Fabozzi, 2024. "Dynamic Asset Pricing in a Unified Bachelier-Black-Scholes-Merton Model," Papers 2405.12479, arXiv.org, revised Jun 2024.

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    More about this item

    Keywords

    Jarrow-Rudd binomial option pricing; Skew random walk; Cherny-Shiryaev-Yor invariance principle; Hedging transaction cost;
    All these keywords.

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation

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