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When Does Extra Risk Strictly Increase the Value of Options?

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  • Eric Rasmusen

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 the Value of Options?," Finance 0409004, University Library of Munich, Germany.
    • Handle: RePEc:wpa:wuwpfi:0409004
    Note: Type of Document - pdf; pages: 20
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    File URL: https://econwpa.ub.uni-muenchen.de/econ-wp/fin/papers/0409/0409004.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. Masaaki Kijima, 2002. "Monotonicity And Convexity Of Option Prices Revisited," Mathematical Finance, Wiley Blackwell, vol. 12(4), pages 411-425, October.
    3. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
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    5. Robert R. Bliss, 2000. "The pitfalls in inferring risk from financial market data," Working Paper Series WP-00-24, Federal Reserve Bank of Chicago.
    6. 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.
    7. Jagannathan, Ravi, 1984. "Call options and the risk of underlying securities," Journal of Financial Economics, Elsevier, vol. 13(3), pages 425-434, September.
    8. Hadar, Josef & Russell, William R, 1969. "Rules for Ordering Uncertain Prospects," American Economic Review, American Economic Association, vol. 59(1), pages 25-34, March.
    9. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    10. 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.
    11. Yaacov Z. Bergman & Bruce D. Grundy & Zvi Wiener, "undated". "General Properties of Option Prices (Revision of 11-95) (Reprint 058)," Rodney L. White Center for Financial Research Working Papers 1-96, Wharton School Rodney L. White Center for Financial Research.
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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.

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    More about this item

    Keywords

    options; risk; mean-preserving spread; calls;
    All these keywords.

    JEL classification:

    • G - Financial Economics

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