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The Theoretical Price of a Share-Based Payment with Performance Conditions and Implications for the Current Accounting Standards

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  • Masahiro Fujimoto

Abstract

Although the growth of share-based payments with performance conditions (hereafter, SPPC) is prominent today, the theoretical price of SPPC has not been sufficiently studied. Reflecting such a situation, the current accounting standards for share-based payments issued in 2004 have had many problems. This paper develops a theoretical SPPC price model with a framework for a marginal utility-based price, which previous studies proposed is the price of contingent claims in an incomplete market. This paper's contribution is fivefold. First, we restricted the stochastic process to a certain class to demonstrate how to consistently change all variables' probability distributions, which affect the SPPC payoff. Second, we explicitly indicated not only the stochastic processes of the stock price process and performance variables under the changed probability, but also how the changes in the performance variables' drift coefficients related to stock betas. Third, we proposed a convenient model in application that uses only a few parameters. Fourth, we provided a method to estimate the parameters and improve the estimation of both the price and parameters. Fifth, we illustrated the problems in current accounting standards and indicated how the theoretical price model can significantly improve them.

Suggested Citation

  • Masahiro Fujimoto, 2018. "The Theoretical Price of a Share-Based Payment with Performance Conditions and Implications for the Current Accounting Standards," Papers 1806.05401, arXiv.org.
    • Handle: RePEc:arx:papers:1806.05401
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    References listed on IDEAS

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    4. David Heath & Robert Jarrow & Andrew Morton, 2008. "Bond Pricing And The Term Structure Of Interest Rates: A New Methodology For Contingent Claims Valuation," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 13, pages 277-305, World Scientific Publishing Co. Pte. Ltd..
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    6. Eugene F. Fama & Kenneth R. French, 2010. "Luck versus Skill in the Cross‐Section of Mutual Fund Returns," Journal of Finance, American Finance Association, vol. 65(5), pages 1915-1947, October.
    7. Schweizer, Martin, 1999. "A guided tour through quadratic hedging approaches," SFB 373 Discussion Papers 1999,96, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
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