Instantaneous liquidity rate, its econometric measurement by volatility feedback

Paul Malliavin; Maria Elvira Mancino

doi:10.1016/S1631-073X(02)02297-5

Instantaneous liquidity rate, its econometric measurement by volatility feedback
[Prime instantanée de liquidité et sa mesure économétrique par les volatilités itérées]

Paul Malliavin ¹ ; Maria Elvira Mancino ²

¹ 10, rue Saint Louis en l'Isle, 75004 Paris, France
² DIMAD, Universitá di Firenze, Via Lombroso 6/17, 50134 Firenze, Italy

Comptes Rendus. Mathématique, Volume 334 (2002) no. 6, pp. 505-508.

Résumé
Abstract

Dans le cas univarié l'existence de la prime instantanée de liquidité est démontrée, ceci indépendamment de toute spécification du modéle ; ce taux donne une mesure quantitative de la stabilité du marché. Nous établissons une formule mathématique donnant la prime instantanée de liquidité en terms de termes de volatilités itérées, qui, pour les valeurs objets d'un nombre élevé de cotations, sont économétriquement mesurables.

In the univariate case we show mathematical existence, in real time and model free, of the instantaneous liquidity rate, which is a measure of the market stability. We give a mathematical formula expressing the instantaneous liquidity rate in terms of self cross volatilities, which, for frequently traded assets, are econometrically measurable.

Reçu le : 2001-12-29
Accepté le : 2002-01-29
Publié le : 2002-01-01

DOI : 10.1016/S1631-073X(02)02297-5

Affiliations des auteurs :

Paul Malliavin ¹ ; Maria Elvira Mancino ²

¹ 10, rue Saint Louis en l'Isle, 75004 Paris, France
² DIMAD, Universitá di Firenze, Via Lombroso 6/17, 50134 Firenze, Italy

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     author = {Paul Malliavin and Maria Elvira Mancino},
     title = {Instantaneous liquidity rate, its econometric measurement by volatility feedback},
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     pages = {505--508},
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     language = {en},
}

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Paul Malliavin; Maria Elvira Mancino. Instantaneous liquidity rate, its econometric measurement by volatility feedback. Comptes Rendus. Mathématique, Volume 334 (2002) no. 6, pp. 505-508. doi : 10.1016/S1631-073X(02)02297-5. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(02)02297-5/

Bibliographie
Cité par

[1] J.C. Cox The constant elasticity of variance option pricing model, J. Portfolio Management, Volume 23 (1997) no. 3, pp. 15-17

[2] A.B. Cruzeiro; P. Malliavin Non perturbative construction of invariant measure through confinement by curvature, J. Math. Pures Appl., Volume 77 (1998), pp. 527-538

[3] J. Fouque; G. Papanicolau; R. Sircar Derivatives in Financial Markets with Stochastic Volatility, Cambridge University Press, 2000

[4] P. Malliavin; M.E. Mancino Fourier series method for measurement of multivariate volatilities, Finance and Stochastics, Volume VI (2002), pp. 49-61

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