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Dynamic Spanning: Are Options An Appropriate Instrument?1

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  • Isabelle Bajeux‐Besnainou
  • Jean‐Charles Rochet

Abstract

Ross (1976) has shown, in a static framework, how options can complete financial markets. This paper examines the possible extensions of Ross's idea in a dynamic setup. Surprisingly enough, we find that the answer is very sensitive to the choice of the stochastic model for the underlying security returns. More specifically we obtain the following results: In a discrete‐time model, classical European options typically become redundant with some probability (Proposition 2.1). Obnly path dependent (“exotic”) options may generate dynamic spanning (Proposition 4.1). In a continuous‐time model with stochastic volatility of the underlying security, and under reasonable assumptions, a European option is always a good instrument for completing markets (Proposition 5.2).

Suggested Citation

  • Isabelle Bajeux‐Besnainou & Jean‐Charles Rochet, 1996. "Dynamic Spanning: Are Options An Appropriate Instrument?1," Mathematical Finance, Wiley Blackwell, vol. 6(1), pages 1-16, January.
    • Handle: RePEc:bla:mathfi:v:6:y:1996:i:1:p:1-16
    DOI: 10.1111/j.1467-9965.1996.tb00110.x
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    Cited by:

    1. Alziary, Benedicte & Decamps, Jean-Paul & Koehl, Pierre-Francois, 1997. "A P.D.E. approach to Asian options: analytical and numerical evidence," Journal of Banking & Finance, Elsevier, vol. 21(5), pages 613-640, May.
    2. Fornari, Fabio & Mele, Antonio, 2001. "Recovering the probability density function of asset prices using garch as diffusion approximations," Journal of Empirical Finance, Elsevier, vol. 8(1), pages 83-110, March.
    3. Mele, Antonio, 2004. "General Properties of Rational Stock-Market Fluctuations," Economics Series 153, Institute for Advanced Studies.
    4. Antonio Mele, 2003. "Fundamental Properties of Bond Prices in Models of the Short-Term Rate," Review of Financial Studies, Society for Financial Studies, vol. 16(3), pages 679-716, July.
    5. Alexandre M. Baptista, 2005. "Options And Efficiency In Multidate Security Markets," Mathematical Finance, Wiley Blackwell, vol. 15(4), pages 569-587, October.
    6. Alexandre Baptista, 2000. "Options and Efficiency in Multiperiod Security Markets," Econometric Society World Congress 2000 Contributed Papers 0299, Econometric Society.
    7. Alziary Chassat, Bénédicte & Takac, Peter, 2017. "On the Heston Model with Stochastic Volatility: Analytic Solutions and Complete Markets," TSE Working Papers 17-796, Toulouse School of Economics (TSE).
    8. C. Mancini, 2002. "The European options hedge perfectly in a Poisson-Gaussian stock market model," Applied Mathematical Finance, Taylor & Francis Journals, vol. 9(2), pages 87-102.
    9. Jovanovic, Franck & Schinckus, Christophe, 2017. "Econophysics and Financial Economics: An Emerging Dialogue," OUP Catalogue, Oxford University Press, number 9780190205034, Decembrie.
    10. E. Jouini & P. -F. Koehl & N. Touzi, 1997. "Incomplete markets, transaction costs and liquidity effects," The European Journal of Finance, Taylor & Francis Journals, vol. 3(4), pages 325-347.

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