Cette série de livres explore les sujets essentiels et les cours optionnels courants proposés dans les programmes de master en finance mathématique et quantitative. Chaque volume est méticuleusement conçu pour être autonome, permettant une étude individuelle, tout en étant étroitement coordonné avec les autres pour un cursus complet. Il offre une exploration rigoureuse des méthodes quantitatives cruciales pour naviguer sur les marchés financiers complexes. Cette ressource est inestimable pour les étudiants et les professionnels cherchant à maîtriser les outils analytiques de la finance moderne.
This brief but full introduction to basic stochastic processes contains key results that have become essential for finance practitioners and provides a solid grounding for understanding the Black-Scholes option pricing model. Students, practitioners and researchers will benefit from the authors' rigorous, but unfussy, approach to technical issues.
This book explains in simple settings the fundamental ideas of financial market modelling and derivative pricing, using the no-arbitrage principle. Relatively elementary mathematics leads to powerful notions and techniques - such as viability, completeness, self-financing and replicating strategies, arbitrage and equivalent martingale measures - which are directly applicable in practice. The general methods are applied in detail to pricing and hedging European and American options within the Cox-Ross-Rubinstein (CRR) binomial tree model. A simple approach to discrete interest rate models is included, which, though elementary, has some novel features. All proofs are written in a user-friendly manner, with each step carefully explained and following a natural flow of thought. In this way the student learns how to tackle new problems.