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- W2017158116 abstract "The Heston model is a popular stock price model with stochastic volatility that has found numerous applications in practice. In the present paper, we study the Riemannian distance function associated with the Heston model and obtain explicit formulas for this function using geometrical and analytical methods. Geometrical approach is based on the study of the Heston geodesics, while the analytical approach exploits the links between the Heston distance function and the Carnot–Carathéodory distance function in the Grushin plane. For the Grushin plane, we establish an explicit formula for the Legendre–Fenchel transform of the limiting cumulant generating function and prove a partial large deviation principle that is true only inside a special set. Le modèle de Heston est un modèle standard pour un actif gouverné par une volatilité stochastique. Ce modèle a trouvé de nombreuses applications dans la pratique. Dans cet article on étudie la distance riemanniene associée au modèle de Heston et on obtient des formules explicites pour cette distance en utlisant des méthodes géométriques ainsi que des méthodes analytiques. L'approche géométrique utilise les géodésiques dans le modèle de Heston, alors que l'approche analytique utilise le lien qui existe entre la distance de Carnot–Carathéodory dans le plan de Grushin et la distance de Heston. Dans le plan de Grushin, on établit une formule explicite pour la transformée de Legendre–Fenchel de la fonction génératrice limite cumulante et on démontre un principe de grandes déviations partielles qui est valable dans un ensemble qu'on identifie." @default.
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- W2017158116 date "2014-03-01" @default.
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- W2017158116 title "The Heston Riemannian distance function" @default.
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- W2017158116 doi "https://doi.org/10.1016/j.matpur.2013.06.004" @default.
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