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Option Pricing by Mathematical Programming

Author

Listed:
  • Flåm, Sjur

    (Economics Department, Bergen University)

Abstract
Financial options typically incorporate times of exercise. Alternatively, they embody set-up costs or indivisibilities. Such features lead to planning problems with integer decision variables. Provided the sample space be finite, it is shown here that integrality constraints can often be relaxed. In fact, simple mathematical programming, aimed at arbitrage or replication, may bound or identify option prices. When the asset market is incomplete, the bounds stem from nonlinear pricing functionals.

Suggested Citation

  • Flåm, Sjur, 2007. "Option Pricing by Mathematical Programming," Working Papers 2007:10, Lund University, Department of Economics.
    • Handle: RePEc:hhs:lunewp:2007_010
    as

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    File URL: http://project.nek.lu.se/publications/workpap/Papers/WP07_10.pdf
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    References listed on IDEAS

    as
    1. Leif Andersen & Mark Broadie, 2004. "Primal-Dual Simulation Algorithm for Pricing Multidimensional American Options," Management Science, INFORMS, vol. 50(9), pages 1222-1234, September.
    2. Laurence Carassus & Miklós Rásonyi, 2006. "Convergence of Utility Indifference Prices to the Superreplication Price," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 64(1), pages 145-154, August.
    3. Klaus Sandmann, 1993. "The Pricing of Options With an Uncertain Interest Rate: A Discrete‐Time Approach1," Mathematical Finance, Wiley Blackwell, vol. 3(2), pages 201-216, April.
    4. repec:bla:jfinan:v:43:y:1988:i:2:p:301-08 is not listed on IDEAS
    5. Evstigneev, I.V. & Flam, S.D., 2000. "Stochastic Programming: Non-Anticipativity and Lagrange Multipliers," Norway; Department of Economics, University of Bergen 1100, Department of Economics, University of Bergen.
    6. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    7. Jaime Cuevas Dermody & R. Tyrrell Rockafellar, 1991. "Cash Stream Valuation In the Face of Transaction Costs and Taxes," Mathematical Finance, Wiley Blackwell, vol. 1(1), pages 31-54, January.
    8. Avinash K. Dixit & Robert S. Pindyck, 1994. "Investment under Uncertainty," Economics Books, Princeton University Press, edition 1, number 5474.
    9. Martin J. Osborne & Ariel Rubinstein, 1994. "A Course in Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262650401, April.
    10. Gyana R. Parija & Shabbir Ahmed & Alan J. King, 2004. "On Bridging the Gap Between Stochastic Integer Programming and MIP Solver Technologies," INFORMS Journal on Computing, INFORMS, vol. 16(1), pages 73-83, February.
    11. Martin B. Haugh & Leonid Kogan, 2004. "Pricing American Options: A Duality Approach," Operations Research, INFORMS, vol. 52(2), pages 258-270, April.
    12. Wolfstetter,Elmar, 2000. "Topics in Microeconomics," Cambridge Books, Cambridge University Press, number 9780521645348, September.
    13. Jitka Dupačová & Giorgio Consigli & Stein Wallace, 2000. "Scenarios for Multistage Stochastic Programs," Annals of Operations Research, Springer, vol. 100(1), pages 25-53, December.
    14. L. C. G. Rogers, 2002. "Monte Carlo valuation of American options," Mathematical Finance, Wiley Blackwell, vol. 12(3), pages 271-286, July.
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    More about this item

    Keywords

    asset pricing; arbitrage; options; finite sample space; scenario tree; equivalent martingale measures; bid-ask intervals; incomplete market; linear programming; combinatorial optimization; totally unimodular matrices.;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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