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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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    1. Levy, Haim, 1985. "Upper and Lower Bounds of Put and Call Option Value: Stochastic Dominance Approach," Journal of Finance, American Finance Association, vol. 40(4), pages 1197-1217, September.
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    7. Mark Rubinstein, 1976. "The Valuation of Uncertain Income Streams and the Pricing of Options," Bell Journal of Economics, The RAND Corporation, vol. 7(2), pages 407-425, Autumn.
    8. Bick, Avi, 1987. "On the Consistency of the Black-Scholes Model with a General Equilibrium Framework," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 22(3), pages 259-275, September.
    9. Stapleton, Richard C & Subrahmanyam, Marti G, 1984. "The Valuation of Options When Asset Returns Are Generated by a Binomial Process," Journal of Finance, American Finance Association, vol. 39(5), pages 1525-1539, December.
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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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