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Dynamic Spanning: Are Options an Appropriate Instrument?

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  • Bajeux, I.
  • Rochet, J.C.

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). Copyright 1996 Blackwell Publishers.

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Bibliographic Info

Paper provided by Toulouse - GREMAQ in its series Papers with number 94.329.

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Length: 24 pages
Date of creation: 1994
Date of revision:
Handle: RePEc:fth:gremaq:94.329

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Keywords: financial market;

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Cited by:
  1. 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.
  2. Ghysels, E. & Harvey, A. & Renault, E., 1995. "Stochastic Volatility," Papers, Toulouse - GREMAQ 95.400, Toulouse - GREMAQ.
  3. F. Fornari & A. Mele, 2000. "Recovering the Probability Density Function of Asset Prices using Garch as Diffusion Approximations," THEMA Working Papers 2000-12, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
  4. Alziary, B. & Decamps, J-P. & Koehl, P-F., 1996. "A P.D.E. Approach to Asian Options: Analytical and Numerical Evidence," Papers, Toulouse - GREMAQ 96.430, Toulouse - GREMAQ.
  5. Antonio Mele, 2004. "General Properties of Rational Stock-Market Fluctuations," Econometric Society 2004 North American Summer Meetings 223, Econometric Society.
  6. Antonio Mele, 2002. "Fundamental Properties of Bond Prices in Models of the Short-Term Rate," Working Papers 460, Queen Mary, University of London, School of Economics and Finance.
  7. Alexandre Baptista, 2000. "Options and Efficiency in Multiperiod Security Markets," Econometric Society World Congress 2000 Contributed Papers 0299, Econometric Society.
  8. C. Mancini, 2002. "The European options hedge perfectly in a Poisson-Gaussian stock market model," Applied Mathematical Finance, Taylor & Francis Journals, Taylor & Francis Journals, vol. 9(2), pages 87-102.

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