Readers will find that, refreshingly, this text presents in a vivid yet concise style the necessary statistical and mathematical background for financial engineers. The focus is both on fundamentals of mathematical finance and financial time series analysis and on applications to given problems of financial markets, making the book the ideal basis for lectures, seminars and crash courses on the topic.

For the second edition the book has been updated and extensively revised. Several new topics have been included, such as a chapter on credit risk management.

Inhalt

Option Pricing.- Derivatives.- to Option Management.- Basic Concepts of Probability Theory.- Stochastic Processes in Discrete Time.- Stochastic Integrals and Differential Equations.- Black-Scholes Option Pricing Model.- Binomial Model for European Options.- American Options.- Exotic Options.- Models for the Interest Rate and Interest Rate Derivatives.- Statistical Models of Financial Time Series.- Introduction: Definitions and Concepts.- ARIMA Time Series Models.- Time Series with Stochastic Volatility.- Non-parametric Concepts for Financial Time Series.- Selected Financial Applications.- Pricing Options with Flexible Volatility Estimators.- Value at Risk and Backtesting.- Copulae and Value at Risk.- Statistics of Extreme Risks.- Neural Networks.- Volatility Risk of Option Portfolios.- Nonparametric Estimators for the Probability of Default.- Credit Risk Management.