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Decreasing Absolute Risk Aversion and Option Pricing Bounds

Author

Listed:
  • Antonella Basso

    (Department of Applied Mathematics, University of Venice, Venice, Italy)

  • Paolo Pianca

    (Department of Applied Mathematics, University of Venice, Venice, Italy)

Abstract

In this paper efficient bounds for the price of a call option are obtained using the decreasing absolute risk aversion (DARA) dominance rule. Such lower and upper bounds are obtained minimizing and maximizing, respectively, the objective function of a nonlinear optimization problem. An explicit formula (related to an exponential utility function) is given for the special case of three states of nature. A large number of experiments have been carried out and the numerical results support the conjecture that the same formula holds for problems with a number of states n

Suggested Citation

  • Antonella Basso & Paolo Pianca, 1997. "Decreasing Absolute Risk Aversion and Option Pricing Bounds," Management Science, INFORMS, vol. 43(2), pages 206-216, February.
    • Handle: RePEc:inm:ormnsc:v:43:y:1997:i:2:p:206-216
    DOI: 10.1287/mnsc.43.2.206
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    Citations

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    Cited by:

    1. Thierry Post & Valerio Potì, 2017. "Portfolio Analysis Using Stochastic Dominance, Relative Entropy, and Empirical Likelihood," Management Science, INFORMS, vol. 63(1), pages 153-165, January.
    2. Thierry Post & Milos Kopa, 2015. "Portfolio Choice based on Third-degree Stochastic Dominance, With an Application to Industry Momentum," Koç University-TUSIAD Economic Research Forum Working Papers 1527, Koc University-TUSIAD Economic Research Forum.
    3. 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.
    4. Post, Thierry, 2016. "Standard Stochastic Dominance," European Journal of Operational Research, Elsevier, vol. 248(3), pages 1009-1020.
    5. Basso, A. & Pianca, P., 2001. "Option pricing bounds with standard risk aversion preferences," European Journal of Operational Research, Elsevier, vol. 134(2), pages 249-260, October.
    6. Lim, Terence & Lo, Andrew W. & Merton, Robert C. & Scholes, Myron S., 2006. "The Derivatives Sourcebook," Foundations and Trends(R) in Finance, now publishers, vol. 1(5–6), pages 365-572, April.
    7. Thierry Post & Yi Fang & Miloš Kopa, 2015. "Linear Tests for Decreasing Absolute Risk Aversion Stochastic Dominance," Management Science, INFORMS, vol. 61(7), pages 1615-1629, July.
    8. Chung, San-Lin & Wang, Yaw-Huei, 2008. "Bounds and prices of currency cross-rate options," Journal of Banking & Finance, Elsevier, vol. 32(5), pages 631-642, May.
    9. Jun-ya Gotoh & Yoshitsugu Yamamoto & Weifeng Yao, 2011. "Bounding Contingent Claim Prices via Hedging Strategy with Coherent Risk Measures," Journal of Optimization Theory and Applications, Springer, vol. 151(3), pages 613-632, December.
    10. Fang, Yi & Post, Thierry, 2017. "Higher-degree stochastic dominance optimality and efficiency," European Journal of Operational Research, Elsevier, vol. 261(3), pages 984-993.
    11. Courtois, Olivier Le & Xu, Xia, 2023. "Semivariance below the maximum: Assessing the performance of economic and financial prospects," Journal of Economic Behavior & Organization, Elsevier, vol. 209(C), pages 185-199.
    12. Thierry Post & Miloš Kopa, 2017. "Portfolio Choice Based on Third-Degree Stochastic Dominance," Management Science, INFORMS, vol. 63(10), pages 3381-3392, October.
    13. Tobias Huber & Johannes G. Jaspersen & Andreas Richter & Dennis Strümpel, 2023. "On the change of risk aversion in wealth: a field experiment in a closed economic system," Experimental Economics, Springer;Economic Science Association, vol. 26(1), pages 1-26, March.
    14. Hsuan-Chu Lin & Ren-Raw Chen & Oded Palmon, 2012. "Non-parametric method for European option bounds," Review of Quantitative Finance and Accounting, Springer, vol. 38(1), pages 109-129, January.
    15. Antonella Basso & Paolo Pianca, 1997. "On the relative efficiency of nth order and DARA stochastic dominance rules," Applied Mathematical Finance, Taylor & Francis Journals, vol. 4(4), pages 207-222.
    16. Jun-ya Gotoh & Hiroshi Konno, 2002. "Bounding Option Prices by Semidefinite Programming: A Cutting Plane Algorithm," Management Science, INFORMS, vol. 48(5), pages 665-678, May.
    17. Basso, A. & Pianca, P., 1999. "A more informative estimation procedure for the parameters of a diffusion process," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 269(1), pages 45-53.

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