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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.
    2. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters,in: Theory Of Valuation, chapter 8, pages 229-288 World Scientific Publishing Co. Pte. Ltd..
    3. Cox, John C. & Ross, Stephen A., 1976. "The valuation of options for alternative stochastic processes," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 145-166.
    4. Kenneth J. Arrow & Anthony C. Fisher, 1974. "Environmental Preservation, Uncertainty, and Irreversibility," The Quarterly Journal of Economics, Oxford University Press, vol. 88(2), pages 312-319.
    5. Jagannathan, Ravi, 1984. "Call options and the risk of underlying securities," Journal of Financial Economics, Elsevier, vol. 13(3), pages 425-434, September.
    6. Hadar, Josef & Russell, William R, 1969. "Rules for Ordering Uncertain Prospects," American Economic Review, American Economic Association, vol. 59(1), pages 25-34, March.
    7. Avinash K. Dixit & Robert S. Pindyck, 1994. "Investment under Uncertainty," Economics Books, Princeton University Press, edition 1, number 5474, June.
    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. 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.

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