RFS Advance Access originally published online on July 14, 2007
Review of Financial Studies 2007 20(5):1647-1667; doi:10.1093/rfs/hhm028
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When Does Extra Risk Strictly Increase an Option's Value?
Indiana University
Address correspondence to Eric Rasmusen Dan, R. and Catherine M. Dalton Professor, Department of Business Economics and Public Policy, Kelley School of Business, Indiana University, BU 456, 1309 E. 10th Street, Bloomington, Indiana, 47405-1701 or e-mail: Erasmuse{at}indiana.edu
JEL: D81, G12
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Abstract |
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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."
I thank Maria Arbatskaya, Jack Meyer, Peter Rangazas, Steve Russell, Yacheng Sun, an anonymous referee, and participants in talks at the 2003 BLISS Conference and Georgia State and DePaul Universities for their comments.