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Minimum option prices under decreasing absolute risk aversion

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  • Kamlesh Mathur
  • Peter Ritchken

Abstract

We establish bounds on option prices in an economy where the representative investor has an unknown utility function that is constrained to belong to the family of nonincreasing absolute risk averse functions. For any distribution of terminal consumption, we identify a procedure that establishes the lower bound of option prices. We prove that the lower bound derives from a particular negative exponential utility function. We also identify lower bounds of option prices in a decreasing relative risk averse economy. For this case, we find that the lower bound is determined by a power utility function. Similar to other recent findings, for the latter case, we confirm that under lognormality of consumption, the Black Scholes price is a lower bound. The main advantage of our bounding methodology is that it can be applied to any arbitrary marginal distribution for consumption. Copyright Kluwer Academic Publishers 1999

Suggested Citation

  • Kamlesh Mathur & Peter Ritchken, 1999. "Minimum option prices under decreasing absolute risk aversion," Review of Derivatives Research, Springer, vol. 3(2), pages 135-156, May.
    • Handle: RePEc:kap:revdev:v:3:y:1999:i:2:p:135-156
    DOI: 10.1023/A:1009602426513
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    References listed on IDEAS

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    2. John Handley, 2005. "On the Upper Bound of a Call Option," Review of Derivatives Research, Springer, vol. 8(2), pages 85-95, August.

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