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On Stochastic Dominance and Decreasing Absolute Risk Averse Option Pricing Bounds

Author

Listed:
  • Peter Ritchken

    (Weatherhead School of Management, Case Western Reserve University, Cleveland, Ohio 44106)

  • Shyanjaw Kuo

    (Weatherhead School of Management, Case Western Reserve University, Cleveland, Ohio 44106)

Abstract

Merton, Perrakis and Ryan, Levy, and Ritchken have established option pricing bounds under first and second stochastic dominance preferences. These bounds are particularly important for valuing contingent claims when continuous trading in the claim and/or underlying security does not exist. This article provides option bounds under higher orders of dominance. Specifically, option bounds are obtained by solving mathematical programs where preference structures on prices are represented by constraints. For first, second, third and higher orders of stochastic dominance preferences, the special linear structure of the mathematical programs allow analytical solutions to be obtained for the bounds. For DARA preferences, third order stochastic dominance, while being necessary, is not sufficient and additional constraints must be imposed. Unfortunately these additional constraints are nonlinear. While in this case closed form analytical solutions for the option bounds are not obtained, numerical examples are presented to illustrate their strength.

Suggested Citation

  • Peter Ritchken & Shyanjaw Kuo, 1989. "On Stochastic Dominance and Decreasing Absolute Risk Averse Option Pricing Bounds," Management Science, INFORMS, vol. 35(1), pages 51-59, January.
    • Handle: RePEc:inm:ormnsc:v:35:y:1989:i:1:p:51-59
    DOI: 10.1287/mnsc.35.1.51
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    Citations

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    Cited by:

    1. 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.
    2. Thierry Post & Iňaki Rodríguez Longarela, 2021. "Risk Arbitrage Opportunities for Stock Index Options," Operations Research, INFORMS, vol. 69(1), pages 100-113, January.
    3. Ryan, Peter J., 2003. "Progressive option bounds from the sequence of concurrently expiring options," European Journal of Operational Research, Elsevier, vol. 151(1), pages 193-223, November.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. Peter Ryan, 2000. "Tighter Option Bounds from Multiple Exercise Prices," Review of Derivatives Research, Springer, vol. 4(2), pages 155-188, May.
    9. 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.
    10. repec:dau:papers:123456789/30 is not listed on IDEAS
    11. 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.

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