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Introduction aux processus d'évolution du prix des actions en temps continu et efficience du marché boursier

Published online by Cambridge University Press:  17 August 2016

Roland Gillet
Roland Gillet*
Affiliation:
Université Catholique de Louvain
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Résumé

L’objet premier du papier est de présenter les principales hypothèses économiques nécessaires à l’élaboration des processus “Itô” de diffusion en temps continu décrivant l’évolution du rendement des actifs financiers. Le papier discute le degré de généralité de ces hypothèses et fournit également une dérivation utile du lemme d’Itô. Dans le contexte de l’efficience du marché financier, il est démontré qu’un processus Itô ne répond pas de façon générale aux propriétés de la martingale ou du “random walk” pas plus qu’il n’implique que les rendements soient nécessairement normalement distribués.

Summary

Summary

The primary focus of the paper is on the main economic assumptions that are sufficient for financial returns to be distributed according to Itô diffusion processes. The paper discusses the degree of generality of these assumptions and also provides a useful derivation of Itô’s lemma. In the context of the efficient market hypothesis it is shown that an Itô process in itself does not imply that prices follow a martingale or a random walk nor that returns are necessarily normally distributed.

Keywords

313313
Type
Research Article
Information
Recherches Économiques de Louvain/ Louvain Economic Review , Volume 57 , Issue 1 , 1991 , pp. 77 - 93
Copyright
Copyright © Université catholique de Louvain, Institut de recherches économiques et sociales 1991 

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Footnotes

*

L'auteur tient à remercier Ronald Anderson, Robert Cobbaut, Benjamin Friedman, Alexis Jacquemin, Albert Minguet, Franco Modigliani, Alain Siaens, ainsi que les participants au séminaire des doctorants à l'Université Catholique de Louvain et au séminaire de finance au Massachusetts Institute of Technology, pour leurs remarques et suggestions. Il est specialement reconnaissant à Robert Merton pour ses nombreux conseils et au Fonds National Belge de la Recherche Scientifique pour son aide financière. De toute évidence, l'auteur conserve seul la responsabilité des erreurs ou imperfections éventuelles.

References

Bibliographie

Bachelier, L. (1900), Theory of specubtion, in Cootner, P. (1964), pp. 17–78.Google Scholar
Black, F. et Scholes, M. (1973), The pricing of options and corporate liabilities, Journal of Political Economy, 9, pp. 637–654.Google Scholar
Clark, P. K. (1973), A subordinated stochastic process model with finite variance for speculative prices, Econometrica, 1, pp. 135–155.Google Scholar
Cootner, P. (1964), The random character of stock market prices, Cambridge, M. I. T. Press.Google Scholar
Cox, D. A. et Miller, H. D. (1968), The theory of stochastic processes, New-York, John Wiley.Google Scholar
Duffie, D. (1988), Security markets: stochastic models, San Diego, Academic Press, Inc.Google Scholar
Fama, E. F. (1970), Efficient capital markets : a review of theory and empirical work, Journal of Finance, 25, pp. 383–417.Google Scholar
Fama, E. F. (1976), Foundations of finance, New-York, Basic Books.Google Scholar
Feller, W. (1966), An introduction to probability theory and its applications, New-York, John Wiley.Google Scholar
Granger, C. W. et Morgenstern, O. (1963), Spectral analysis of New-York stock market prices, in Cootner, P. (1964), pp. 162–188.Google Scholar
Harrison, J. M. (1985), Brownian motion and stochastic flow systems, New-York, John Wiley.Google Scholar
Huang, C. F. et Litzenberger, R. H. (1988), Foundations for financial economics, New-York, North-Holland.Google Scholar
Ingersoll, J. E. (1987), Theory of financial decision making, Maryland, Rowman and Littlefield.Google Scholar
Kendall, M. G. (1953), The analysis of economic time-series, in Cootner, P. (1964), pp. 85–99.Google Scholar
Leroy, S. F. (1989), Efficient capital markets and martingales, Journal of Economic Literature, 27, pp. 1583–1621.Google Scholar
Merton, R. C. (1971), Optimum consumption and portfolio rules in a continuous-time model, Journal of Economic Theory, 3, pp. 373–413.Google Scholar
Merton, R. C. (1973), An intertemporal capital asset pricing model, Econometrica, 41, pp. 867–887.Google Scholar
Merton, R. C. (1975), Theory of finance from the perspective of continuous time, Journal of Financial and Quantitative Analysis, 10, pp. 659–674.Google Scholar
Merton, R. C. (1976), Option pricing when underlying stock returns are discontinuous, Journal of Financial Economics, 3, pp. 125–144.Google Scholar
Merton, R. C. (1980), On estimating the expected return on the market: an exploratory investigation, Journal of Financial Economics, 8, pp. 323–361.Google Scholar
Merton, R. C. (1982), On the mathematics and economics assumptions of continuous-time models, in Sharpe, W. F. and Cootner, C. M., Financial economics: Essays in Honor of Paul Cootner, New Jersey, Prentice Hall, pp. 26–49.Google Scholar
Merton, R. C. (1990), Continuous-time finance, Cambridge, Basil Black-well.Google Scholar
Ramanathan, R. (1989), Introductory econometrics with applications, San Diego, Harcourt Brace Jovanovich, Publ.Google Scholar
Roberts, H. (1967), Statistical versus clinical prediction of the stock market, Chicago, Unpublished Paper.Google Scholar
Rosenfeld, E. (1980), Stochastic processes of common stock returns: an empirical examination, Ph. D. Dissertation, Sloan School of Management, M. I. T.Google Scholar
Samuelson, P. A. (1965), Proof that properly anticipated prices fluctuate randomly, Industrial Management Review, 6, pp. 41–49.Google Scholar
Samuelson, P. A. (1973), Proof that properly discounted percent values of assets vibrate randomly, Bell Journal of Economics and Management Science, 4, pp. 369–374.Google Scholar