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Arbitrages and Arrow-Debreu Prices

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  • Gaia Barone

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    (Università LUISS “Guido Carli”)

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    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.

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    File URL: http://www.rivistapoliticaeconomica.it/2008/nov-dic/pdf/Barone_en.pdf
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    Bibliographic Info

    Article provided by SIPI Spa in its journal Rivista di Politica Economica.

    Volume (Year): 98 (2008)
    Issue (Month): 6 (November-December)
    Pages: 43-78

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    Handle: RePEc:rpo:ripoec:v:98:y:2008:i:6:p:43-78

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    Related research

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

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    1. Myron S. Scholes & Mark A. Wolfson, 1989. "Decentralized Investment Banking: The Case of Discount Dividend-Reinve stment and Stock-Purchase Plans," NBER Working Papers 3093, National Bureau of Economic Research, Inc.
    2. Rubinstein, Mark, 1994. " Implied Binomial Trees," Journal of Finance, American Finance Association, vol. 49(3), pages 771-818, July.
    3. Lars Peter Hansen & Ravi Jagannathan, 1990. "Implications of security market data for models of dynamic economies," Discussion Paper / Institute for Empirical Macroeconomics 29, Federal Reserve Bank of Minneapolis.
    4. 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 449-70, May.
    5. 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.
    6. 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.
    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. 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.
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