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.

Reçu le :
Accepté le :
Publié le :
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 
@article{CRMATH_2002__334_6_505_0,
     author = {Malliavin, Paul and Mancino, Maria Elvira},
     title = {Instantaneous liquidity rate, its econometric measurement by volatility feedback},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {505--508},
     publisher = {Elsevier},
     volume = {334},
     number = {6},
     year = {2002},
     doi = {10.1016/S1631-073X(02)02297-5},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1016/S1631-073X(02)02297-5/}
}
TY  - JOUR
AU  - Malliavin, Paul
AU  - Mancino, Maria Elvira
TI  - Instantaneous liquidity rate, its econometric measurement by volatility feedback
JO  - Comptes Rendus. Mathématique
PY  - 2002
SP  - 505
EP  - 508
VL  - 334
IS  - 6
PB  - Elsevier
UR  - http://archive.numdam.org/articles/10.1016/S1631-073X(02)02297-5/
DO  - 10.1016/S1631-073X(02)02297-5
LA  - en
ID  - CRMATH_2002__334_6_505_0
ER  - 
%0 Journal Article
%A Malliavin, Paul
%A Mancino, Maria Elvira
%T Instantaneous liquidity rate, its econometric measurement by volatility feedback
%J Comptes Rendus. Mathématique
%D 2002
%P 505-508
%V 334
%N 6
%I Elsevier
%U http://archive.numdam.org/articles/10.1016/S1631-073X(02)02297-5/
%R 10.1016/S1631-073X(02)02297-5
%G en
%F CRMATH_2002__334_6_505_0
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://archive.numdam.org/articles/10.1016/S1631-073X(02)02297-5/

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

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

[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

Cité par Sources :