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When Does Extra Risk Strictly Increase an Option's Value?

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  • Eric Rasmusen

    (Department of Business Economics and Public Policy, Indiana University Kelley School of Business)

Abstract

It is well known that risk increases the value of options. This paper makes that precise in a new way. The conventional theorem says that the value of an option does not fall if the underlying option becomes riskier in the conventional sense of the mean-preserving spread. This paper uses two new definitions of "riskier" to show that the value of an option strictly increases (a) if the underlying asset becomes "pointwise riskier," and (b) only if the underlying asset becomes "extremum riskier."

Suggested Citation

  • Eric Rasmusen, 2004. "When Does Extra Risk Strictly Increase an Option's Value?," Working Papers 2004-12, Indiana University, Kelley School of Business, Department of Business Economics and Public Policy.
    • Handle: RePEc:iuk:wpaper:2004-12
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    File URL: http://kelley.iu.edu/riharbau/RePEc/iuk/wpaper/bepp2004-12-rasmusen.pdf
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    References listed on IDEAS

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    1. Bergman, Yaacov Z & Grundy, Bruce D & Wiener, Zvi, 1996. "General Properties of Option Prices," Journal of Finance, American Finance Association, vol. 51(5), pages 1573-1610, December.
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    5. Jagannathan, Ravi, 1984. "Call options and the risk of underlying securities," Journal of Financial Economics, Elsevier, vol. 13(3), pages 425-434, September.
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    8. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    9. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
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    Cited by:

    1. Eric Rasmusen, 2004. "Getting Carried Away in Auctions as Imperfect Value Discovery," Industrial Organization 0409001, University Library of Munich, Germany.
    2. Kuersten, Wolfgang & Linde, Rainer, 2011. "Corporate hedging versus risk-shifting in financially constrained firms: The time-horizon matters!," Journal of Corporate Finance, Elsevier, vol. 17(3), pages 502-525, June.
    3. Olivier Gossner & Christoph Kuzmics, 2019. "Preferences Under Ignorance," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 60(1), pages 241-257, February.
    4. Jonathan Goldberg, 2014. "Idiosyncratic Investment Risk and Business Cycles," Finance and Economics Discussion Series 2014-05, Board of Governors of the Federal Reserve System (U.S.).

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