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Local volatility dynamic models
Authors:René Carmona  Sergey Nadtochiy
Institution:(1) Bendheim Center for Finance, ORFE, Princeton University, Princeton, NJ 08544, USA;(2) Dept. ORFE, Princeton University, Princeton, NJ 08544, USA
Abstract:This paper is concerned with the characterization of arbitrage-free dynamic stochastic models for the equity markets when Itô stochastic differential equations are used to model the dynamics of a set of basic instruments including, but not limited to, the underliers. We study these market models in the framework of the HJM philosophy originally articulated for Treasury bond markets. The main thrust of the paper is to characterize absence of arbitrage by a drift condition and a spot consistency condition for the coefficients of the local volatility dynamics.
Keywords:Implied volatility surface  Local volatility surface  Market models  Arbitrage-free term structure dynamics  Heath–  Jarrow–  Morton theory
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