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Dynamic Spanning: Are Options An Appropriate Instrument?

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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). Copyright 1996 Blackwell Publishers.

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Bibliographic Info

Article provided by Wiley Blackwell in its journal Mathematical Finance.

Volume (Year): 6 (1996)
Issue (Month): 1 ()
Pages: 1-16

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Handle: RePEc:bla:mathfi:v:6:y:1996:i:1:p:1-16

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Web page: http://www.blackwellpublishing.com/journal.asp?ref=0960-1627

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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. Fabio Fornari & Antonio Mele, 2001. "Recovering the Probability Density Function of Asset Prices Using GARCH as Diffusion Approximations," Temi di discussione (Economic working papers) 396, Bank of Italy, Economic Research and International Relations Area.
  3. Antonio Mele, 2004. "General Properties of Rational Stock-Market Fluctuations," Econometric Society 2004 North American Summer Meetings 223, Econometric Society.
  4. 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.
  5. 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.
  6. Ghysels, E. & Harvey, A. & Renault, E., 1996. "Stochastic Volatility," Cahiers de recherche 9613, Universite de Montreal, Departement de sciences economiques.
  7. Alexandre Baptista, 2000. "Options and Efficiency in Multiperiod Security Markets," Econometric Society World Congress 2000 Contributed Papers 0299, Econometric Society.
  8. 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.

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