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Options with Constant Underlying Elasticity in Strikes

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Abstract

Closed-form solutions are derived and interpreted for European options, with stochastic strike prices, that maintain constant elasticity of the strike with respect to the price of the underlying asset. We refer to such options as CUES. CUES preserve the relative shares of exercise price risk for both the buyer and writer of the option, regardless of whether the price of the underlying asset moves up or down. The relevance of the CUES concept is established through applications in two distinct fields. First, it is established that CUES-like options are embedded in private equity investments. This concept is then used in a novel application to determine the equity share of a private company corresponding to a given level of investment. Secondly, the advantages that CUES would provide over traditional executive stock option grants are considered and it is shown that CUES can provide enhanced incentive-alignment without increasing options expense to the company.

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Authors and Affiliations

  1. Department of Finance and Business Law, University of North Carolina at Charlotte, USA

    Lloyd P. Blenman & Steven P. Clark

Authors
  1. Lloyd P. Blenman
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  2. Steven P. Clark
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Correspondence to Lloyd P. Blenman.

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JEL Classification: G130

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Blenman, L.P., Clark, S.P. Options with Constant Underlying Elasticity in Strikes. Rev Deriv Res 8, 67–83 (2005). https://doi.org/10.1007/s11147-005-3850-z

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  • DOI: https://doi.org/10.1007/s11147-005-3850-z

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