ABSTRACT
Abstract We review the main notions and results in the stochastic calculus of variations, commonly called Malliavin calculus and developed by Malliavin in 1976 in order to give a probabilistic proof of the “sums of squares” Ho¨rmander theorem. In the last section, we focus on various applications: The convexity adjustment of CMS option, the probabilistic representation of sensitivities and the calibration of stochastic volatility models.
