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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."

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File URL: http://www.bus.indiana.edu/riharbau/RePEc/iuk/wpaper/bepp2004-12-rasmusen.pdf
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Bibliographic Info

Paper provided by Indiana University, Kelley School of Business, Department of Business Economics and Public Policy in its series Working Papers with number 2004-12.

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Date of creation: 2004
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Publication status: Forthcoming in Review of Financial Studies
Handle: RePEc:iuk:wpaper:2004-12

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  1. Hadar, Josef & Russell, William R, 1969. "Rules for Ordering Uncertain Prospects," American Economic Review, American Economic Association, vol. 59(1), pages 25-34, March.
  2. Merton, Robert C., 1975. "Option pricing when underlying stock returns are discontinuous," Working papers 787-75., Massachusetts Institute of Technology (MIT), Sloan School of Management.
  3. 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 637-54, May-June.
  4. Jagannathan, Ravi, 1984. "Call options and the risk of underlying securities," Journal of Financial Economics, Elsevier, vol. 13(3), pages 425-434, September.
  5. Arrow, Kenneth J & Fisher, Anthony C, 1974. "Environmental Preservation, Uncertainty, and Irreversibility," The Quarterly Journal of Economics, MIT Press, vol. 88(2), pages 312-19, May.
  6. 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.
  7. Robert C. Merton, 1973. "Theory of Rational Option Pricing," Bell Journal of Economics, The RAND Corporation, vol. 4(1), pages 141-183, Spring.
  8. 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.
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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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