Instantaneous liquidity rate, its econometric measurement by volatility feedback
[Prime instantanée de liquidité et sa mesure économétrique par les volatilités itérées]
Malliavin, Paul1 ; Mancino, Maria Elvira2
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, Tome 334 (2002) no. 6, pp. 505-508.

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.

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DOI : 10.1016/S1631-073X(02)02297-5
Malliavin, Paul 1 ; Mancino, Maria Elvira 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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Malliavin, Paul; Mancino, Maria Elvira. Instantaneous liquidity rate, its econometric measurement by volatility feedback. Comptes Rendus. Mathématique, Tome 334 (2002) no. 6, pp. 505-508. doi : 10.1016/S1631-073X(02)02297-5. http://www.numdam.org/articles/10.1016/S1631-073X(02)02297-5/

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

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

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