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Error Calculus and Path Sensitivity in Financial Models
Authors:Nicolas  Bouleau
Institution:Ecole des Ponts, Paris
Abstract:In the framework of risk management, for the study of the sensitivity of pricing and hedging in stochastic financial models to changes of parameters and to perturbations of the stock prices, we propose an error calculus that is an extension of the Malliavin calculus based on Dirichlet forms. Although useful also in physics, this error calculus is well adapted to stochastic analysis and seems to be the best practicable in finance. This tool is explained here intuitively and with some simple examples.
Keywords:error calculus  risk management  Black-Scholes model  level dependent volatility  sensitivity  Greeks  Malliavin calculus  gradient  Ornstein-Uhlenbeck process  Dirichlet forms  Wiener space  carré du champ
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