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Options and Efficiency in Multiperiod Security Markets

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  • Alexandre Baptista

    (University of Arizona and University of Minnesota)

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    Abstract

    We extend the result of Ross (1976) that European options generate complete markets from the single-period to a multiperiod setting. We find that multiperiod European options on a trading strategy generate dynamic completeness for every arbitrage-free price process, provided that the trading strategy has non-negative terminal dividends and separates states at the terminal date. Furthermore, we show that if the uncertainty and information structure in an economy are such that the number of immediate successors of every non-terminal event is non-decreasing over time, then multiperiod European options on a trading strategy generate dynamic completeness for almost every arbitrage-free price process under a significantly weaker condition on the trading strategy's terminal dividends. This condition requires the trading strategy to have non- negative terminal dividends and to separate states at the terminal date conditional on the information available at the previous date. Finally, we examine the minimum number of options generating dynamic completeness for almost every arbitrage-free price process.

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    Bibliographic Info

    Paper provided by Econometric Society in its series Econometric Society World Congress 2000 Contributed Papers with number 0299.

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    Date of creation: 01 Aug 2000
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    Handle: RePEc:ecm:wc2000:0299

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    1. Kahn, Charles M & Krasa, Stefan, 1993. "Non-existence and Inefficiency of Equilibria with American Options," Economic Theory, Springer, vol. 3(1), pages 169-76, January.
    2. Detemple, Jerome B & Selden, Larry, 1991. "A General Equilibrium Analysis of Option and Stock Market Interactions," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 32(2), pages 279-303, May.
    3. David M. Kreps, 1982. "Multiperiod Securities and the Efficient Allocation of Risk: A Comment on the Black-Scholes Option Pricing Model," NBER Chapters, in: The Economics of Information and Uncertainty, pages 203-232 National Bureau of Economic Research, Inc.
    4. Nils H. Hakansson., 1978. "Welfare Aspects of Options and Supershares," Research Program in Finance Working Papers 68, University of California at Berkeley.
    5. Gabrielle Demange & Guy Laroque, 1999. "Efficiency and options on the market index," Economic Theory, Springer, vol. 14(1), pages 227-235.
    6. Friesen, Peter H, 1979. "The Arrow-Debreu Model Extended to Financial Markets," Econometrica, Econometric Society, vol. 47(3), pages 689-707, May.
    7. Breeden, Douglas T & Litzenberger, Robert H, 1978. "Prices of State-contingent Claims Implicit in Option Prices," The Journal of Business, University of Chicago Press, vol. 51(4), pages 621-51, October.
    8. Isabelle Bajeux-Besnainou & Jean-Charles Rochet, 1996. "Dynamic Spanning: Are Options An Appropriate Instrument?," Mathematical Finance, Wiley Blackwell, vol. 6(1), pages 1-16.
    9. John, Kose, 1981. "Efficient Funds in a Financial Market with Options: A New Irrelevance Proposition," Journal of Finance, American Finance Association, vol. 36(3), pages 685-95, June.
    10. Polemarchakis, H. M. & Ku, Bon-Il, 1990. "Options and equilibrium," Journal of Mathematical Economics, Elsevier, vol. 19(1-2), pages 107-112.
    11. Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, vol. 7(3), pages 229-263, September.
    12. Banz, Rolf W & Miller, Merton H, 1978. "Prices for State-contingent Claims: Some Estimates and Applications," The Journal of Business, University of Chicago Press, vol. 51(4), pages 653-72, October.
    13. Donald J. Brown & Stephen A. Ross, 1988. "Spanning, Valuation and Options," Cowles Foundation Discussion Papers 873, Cowles Foundation for Research in Economics, Yale University.
    14. Green, Richard C. & Jarrow, Robert A., 1987. "Spanning and completeness in markets with contingent claims," Journal of Economic Theory, Elsevier, vol. 41(1), pages 202-210, February.
    15. John, Kose, 1984. "Market Resolution and Valuation in Incomplete Markets," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 19(01), pages 29-44, March.
    16. Hakansson, Nils H, 1978. "Welfare Aspects of Options and Supershares," Journal of Finance, American Finance Association, vol. 33(3), pages 759-76, June.
    17. Magill, Michael J. P. & Shafer, Wayne J., 1990. "Characterisation of generically complete real asset structures," Journal of Mathematical Economics, Elsevier, vol. 19(1-2), pages 167-194.
    18. Ross, Stephen A, 1976. "Options and Efficiency," The Quarterly Journal of Economics, MIT Press, vol. 90(1), pages 75-89, February.
    19. Breeden, Douglas T., 1984. "Futures markets and commodity options: Hedging and optimality in incomplete markets," Journal of Economic Theory, Elsevier, vol. 32(2), pages 275-300, April.
    20. Arditti, Fred D. & John, Kose, 1980. "Spanning the State Space with Options," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 15(01), pages 1-9, March.
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