Malliavin Calculus in Finance

guide to the applications of the Malliavin calculus to finance. Starting with classical questions of non-arbitrage pricing and the Black-Scholes formula, the authors smoothly continue with volatility processes, studying, in particular, implied, spot and local volatilities. Various models with stochastic volatilities are considered, including models based on fractional Brownian motion and rough volatilities. Variance swaps and the VIX, volatility, and other types of swaps are studied. Then the main tools of Malliavin calculus are presented, together with applications of Malliavin calculus to the implied volatility surface and the implied volatility of non-vanilla options. So, the book is very promising for both mathematicians and practitioners and both mathematicians and practitioners will enjoy the beauty of the mathematical description of the world of real finance."
- Yuliya Mishura, Taras Shevchenko National University of Kyiv