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

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Author Info
Eric Rasmusen

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Abstract

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

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File URL: http://hdl.handle.net/10.1093/rfs/hhm028
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Article provided by Oxford University Press for Society for Financial Studies in its journal The Review of Financial Studies.

Volume (Year): 20 (2007)
Issue (Month): 5 (200714)
Pages: 1647-1667
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Handle: RePEc:oup:rfinst:v:20:y:2007:i:5:p:1647-1667

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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. [Downloadable!] (restricted)
  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. [Downloadable!]
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  3. Robert C. Merton, 1973. "Theory of Rational Option Pricing," Bell Journal of Economics, The RAND Corporation, vol. 4(1), pages 141-183, Spring. [Downloadable!] (restricted)
  4. 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. [Downloadable!] (restricted)
  5. 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. [Downloadable!] (restricted)
  6. 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. [Downloadable!] (restricted)
  7. 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. [Downloadable!] (restricted)
  8. Jagannathan, Ravi, 1984. "Call options and the risk of underlying securities," Journal of Financial Economics, Elsevier, vol. 13(3), pages 425-434, September. [Downloadable!] (restricted)
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