Front Cover ; Stochastic Models of Financial Mathematics; Copyright ; Contents; Preface; Notations; Chapter 1. Overview of the Basics of Stochastic Analysis; 1.1. Brownian motion; 1.2. Stochastic integrals; 1.3. Martingales, Itô processes and general Itô's formula; 1.4. Stochastic differential equations; 1.5. Change of probability: the Girsanov theorem; Chapter 2. The Black-Scholes Model; 2.1. Introduction: what is an option?; 2.2. Self-financing strategies; 2.3. Option pricing problem: the Black-Scholes model; 2.4. The Black-Scholes formula
2.5. Risk-neutral probabilities: alternative derivation of the Black-Scholes formula2.6. American options in the Black-Scholes model; 2.7. Exotic options; Chapter 3. Models of Interest Rates; 3.1. Modeling principles; 3.2. The Vašíček model; 3.3. The Cox-Ingersoll-Ross model; 3.4. The Heath-Jarrow-Morton model; Bibliography; Index; Back Cover
