Correlations and bounds for stochastic volatility models

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 “...

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Bibliographic Details
Published inAnnales de l'Institut Henri Poincaré. Analyse non linéaire Vol. 24; no. 1; pp. 1 - 16
Main Authors Lions, P.-L., Musiela, M.
Format Journal Article
LanguageEnglish
Published Paris Elsevier Masson SAS 01.01.2007
Elsevier
EMS
Subjects
Applications
Exact sciences and technology
General Mathematics
Insurance, economics, finance
Mathematical analysis
Mathematics
Multivariate analysis
Ordinary differential equations
Probability and statistics
Sciences and techniques of general use
Statistics
Stochastic model
Correlation
Necessary and sufficient condition
Differential equation
Finance
Stochastic volatility
Stochastic equation
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Summary: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 Lp solutions (for 1<p<∞).
ISSN:0294-1449
1873-1430
DOI:10.1016/j.anihpc.2005.05.007