This book covers the theory of derivatives pricing and hedging as well as techniques used in mathematical finance. The authors use a top-down approach, starting with fundamentals before moving to applications, and present theoretical developments alongside various exercises, providing many examples of practical interest.A large spectrum of concepts and mathematical tools that are usually found in separate monographs are presented here. In addition to the no-arbitrage theory in full generality, this book also explores models and practical hedging and pricing issues. Fundamentals and Advanced Techniques in Derivatives Hedging further introduces advanced methods in probability and analysis, including Malliavin calculus and the theory of viscosity solutions, as well as the recent theory of stochastic targets and its use in risk management, making it the first textbook covering this topic. Graduate students in applied mathematics with an understanding of probability theory and stochastic calculus will find this book useful to gain a deeper understanding of fundamental concepts and methods in mathematical finance.
Bruno Bouchard is Professor of Mathematics at Universite Paris-Dauphine. He is a renowned specialist in mathematical finance and stochastic control. He has been teaching arbitrage theory, option hedging techniques and stochastic control for more than ten years at French universities and engineering schools. Jean-Francois Chassagneux is a professor at the Department of Mathematics at Universite Paris Diderot. He specialises in non-linear pricing methods and associated numerical techniques. He has been teaching mathematical finance for many years at several institutions: Ecole Nationale de la Statistique et de l'Administration Economique, Universite d'Evry, Imperial College London and Universite Paris Diderot.
Part A. Fundamental theorems.- Discrete time models.- Continuous time models.- Optimal management and price selection.- Part B. Markovian models and PDE approach.- Delta hedging in complete market.- Super-replication and its practical limits.- Hedging under loss contraints.- Part C. Practical implementation in local and stochastic volatility models.- Local volatility models.- Stochastic volatility models.- References.