I Interest Rates -- II Financial Products -- III The No-Arbitrage Principle -- IV European and American Options -- The Binomial Option Pricing Model -- VI The Black-Scholes Model -- VII The Black-Scholes Formula -- VIII Stock-Price Models -- IX Interest Rate Models and the Valuation of Interest Rate Derivatives -- X Numerical Tools -- XI Simulation Methods -- XII Calibrating Models – Inverse Problems -- XIII Case Studies: Exotic Derivatives -- XIV Portfolio-Optimization -- XV Introduction to Credit Risk Models.

Swaps, futures, options, structured instruments - a wide range of derivative products is traded in today's financial markets. Analyzing, pricing and managing such products often requires fairly sophisticated quantitative tools and methods. This book serves as an introduction to financial mathematics with special emphasis on aspects relevant in practice. In addition to numerous illustrative examples, algorithmic implementations are demonstrated using "Mathematica" and the software package "UnRisk" (available for both students and teachers). The content is organized in 15 chapters that can be treated as independent modules. In particular, the exposition is tailored for classroom use in a Bachelor or Master program course, as well as for practitioners who wish to further strengthen their quantitative background.