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Arbitrages and Arrow-Debreu Prices

Author

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  • Gaia Barone

    () (Università LUISS “Guido Carli”)

Abstract

The goal of this work is to check that there are no arbitrage opportunities in the CBOE market for S&P500 options and to extract from these options’ quotes the state-price density consistent with the Merton model. The structure of the article is as follows: in Section 2 we examine the relations between arbitrages and Arrow-Debreu prices; in Section 3 we consider two models which seem to be consistent with the market prices of index options: the CEV model and the Merton model; finally, in Section 4 we estimate the state-price density consistent with the Merton-Geske model. Some conclusions follow.

Suggested Citation

  • Gaia Barone, 2008. "Arbitrages and Arrow-Debreu Prices," Rivista di Politica Economica, SIPI Spa, vol. 98(6), pages 43-78, November-.
  • Handle: RePEc:rpo:ripoec:v:98:y:2008:i:6:p:43-78
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    References listed on IDEAS

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    1. Hansen, Lars Peter & Jagannathan, Ravi, 1991. "Implications of Security Market Data for Models of Dynamic Economies," Journal of Political Economy, University of Chicago Press, vol. 99(2), pages 225-262, April.
    2. Merton, Robert C, 1974. "On the Pricing of Corporate Debt: The Risk Structure of Interest Rates," Journal of Finance, American Finance Association, vol. 29(2), pages 449-470, May.
    3. Scholes, Myron S. & Wolfson, Mark A., 1989. "Decentralized investment banking : The case of discount dividend-reinvestment and stock-purchase plans," Journal of Financial Economics, Elsevier, vol. 24(1), pages 7-35, September.
    4. Geske, Robert, 1977. "The Valuation of Corporate Liabilities as Compound Options," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(04), pages 541-552, November.
    5. 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 621-651, October.
    6. Rubinstein, Mark, 1994. " Implied Binomial Trees," Journal of Finance, American Finance Association, vol. 49(3), pages 771-818, July.
    7. Garman, Mark B., 1976. "An algebra for evaluating hedge portfolios," Journal of Financial Economics, Elsevier, vol. 3(4), pages 403-427, October.
    8. Mark Rubinstein., 1994. "Implied Binomial Trees," Research Program in Finance Working Papers RPF-232, University of California at Berkeley.
    9. 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 653-672, October.
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    More about this item

    Keywords

    state-price density; index options; Merton-Geske model;

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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