JournalsaihpcVol. 24, No. 1pp. 1–16

Correlations and bounds for stochastic volatility models

  • P.-L. Lions

    Collège de France, 3, rue d'Ulm, 75005 Paris, France, CEREMADE – UMR C.N.R.S. 7534, Université Paris-Dauphine, place du Maréchal de Lattre de Tassigny, 75775 Paris cedex 16, France
  • M. Musiela

    FIRST, BNP-Paribas, 10 Harewood Avenue, London NW1 6AA, United Kingdom
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Abstract

We investigate here, systematically and rigorously, various stochastic volatility models used in Mathematical Finance. Mathematically, such models involve coupled stochastic differential equations with coefficients that do not obey the natural and classical conditions required to make these models “well-posed”. And we obtain necessary and sufficient conditions on the parameters, such as correlation, of these models in order to have integrable or LpL^{p} solutions (for 1<p<1 < p < \infty ).

Cite this article

P.-L. Lions, M. Musiela, Correlations and bounds for stochastic volatility models. Ann. Inst. H. Poincaré Anal. Non Linéaire 24 (2007), no. 1, pp. 1–16

DOI 10.1016/J.ANIHPC.2005.05.007