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Option Pricing in an Incomplete Market

Author

Listed:
  • Karen Grigorian

    (Department of Statistics and Applied Probability, University of California, Santa Barbara, CA 93106, USA)

  • Robert A. jarrow

    (Samuel Curtis Johnson Graduate School of Management, Cornell University, Ithaca, NY 14853, USA)

Abstract

The purpose of this paper is to illustrate the pricing of options in an incomplete market using the new consistent uplifted martingale measure methodology introduced by Grigorian and Jarrow [2024, Filtration Reduction and Incomplete Markets, Frontiers of Mathematical Finance, 3(1), 78–105; 2023, Filtration Reduction and Completeness in Brownian Motion Models. Working Paper, Cornell University; 2024, Filtration Reduction and Completeness in Jump-Diffusion Models. Working Paper, Cornell University]. We apply it to an incomplete market where a stock has stochastic volatility. Two valuation formulas are generated, depending upon whether the trader is more concerned about volatility or price risk in the construction of a partial replicating portfolio for the option’s payoff.

Suggested Citation

  • Karen Grigorian & Robert A. jarrow, 2024. "Option Pricing in an Incomplete Market," Quarterly Journal of Finance (QJF), World Scientific Publishing Co. Pte. Ltd., vol. 14(03), pages 1-16, September.
    • Handle: RePEc:wsi:qjfxxx:v:14:y:2024:i:03:n:s2010139224500095
    DOI: 10.1142/S2010139224500095
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    More about this item

    Keywords

    Option pricing; incomplete markets; martingale measures; risk-neutral valuation;
    All these keywords.

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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