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SDP Relaxation of Arbitrage Pricing Bounds Based on Option Prices and Moments

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  • J. A. Primbs

    (Management Science and Engineering)

Abstract

This paper develops a semidefinite programming approach to computing bounds on the range of allowable absence of arbitrage prices for a European call option when option prices at other strikes and expirations are available and when moment related information on the underlying is known. The moment related information is incorporated in the problem through the fictitious prices of polynomial valued securities. The optimization then comes from relaxing a risk neutral pricing optimization problem in terms of moments of measures from a decomposition of the risk neutral pricing measure. We demonstrate this optimization formulation with computations using moment data from the standard Black-Scholes option pricing model and Merton’s jump diffusion model.

Suggested Citation

  • J. A. Primbs, 2010. "SDP Relaxation of Arbitrage Pricing Bounds Based on Option Prices and Moments," Journal of Optimization Theory and Applications, Springer, vol. 144(1), pages 137-155, January.
    • Handle: RePEc:spr:joptap:v:144:y:2010:i:1:d:10.1007_s10957-009-9605-5
    DOI: 10.1007/s10957-009-9605-5
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    References listed on IDEAS

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    1. Dimitris Bertsimas & Ioana Popescu, 2002. "On the Relation Between Option and Stock Prices: A Convex Optimization Approach," Operations Research, INFORMS, vol. 50(2), pages 358-374, April.
    2. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    3. Mark H. A. Davis & David G. Hobson, 2007. "The Range Of Traded Option Prices," Mathematical Finance, Wiley Blackwell, vol. 17(1), pages 1-14, January.
    4. Peter Laurence & Tai-Ho Wang, 2005. "Sharp Upper and Lower Bounds for Basket Options," Applied Mathematical Finance, Taylor & Francis Journals, vol. 12(3), pages 253-282.
    5. James E. Smith, 1995. "Generalized Chebychev Inequalities: Theory and Applications in Decision Analysis," Operations Research, INFORMS, vol. 43(5), pages 807-825, October.
    6. Carr, Peter & Madan, Dilip B., 2005. "A note on sufficient conditions for no arbitrage," Finance Research Letters, Elsevier, vol. 2(3), pages 125-130, September.
    7. 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.
    8. Alexandre d'Aspremont & Laurent El Ghaoui, 2003. "Static Arbitrage Bounds on Basket Option Prices," Papers math/0302243, arXiv.org, revised Oct 2005.
    9. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    10. Lo, Andrew W., 1987. "Semi-parametric upper bounds for option prices and expected payoffs," Journal of Financial Economics, Elsevier, vol. 19(2), pages 373-387, December.
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    Cited by:

    1. Roy H. Kwon & Jonathan Y. Li, 2016. "A stochastic semidefinite programming approach for bounds on option pricing under regime switching," Annals of Operations Research, Springer, vol. 237(1), pages 41-75, February.
    2. Peña, Javier & Vera, Juan C. & Zuluaga, Luis F., 2012. "Computing arbitrage upper bounds on basket options in the presence of bid–ask spreads," European Journal of Operational Research, Elsevier, vol. 222(2), pages 369-376.
    3. Roy Kwon & Jonathan Li, 2016. "A stochastic semidefinite programming approach for bounds on option pricing under regime switching," Annals of Operations Research, Springer, vol. 237(1), pages 41-75, February.

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