Interest-Rate Management

Who gains all his ends did set the level too low. Although the history of trading on financial markets started a long and possibly not exactly definable time ago, most financial analysts agree that the core of mathematical finance dates back to the year 1973. Not only did the world's first option exchange open its doors in Chicago in that year but Black and Scholes published their pioneering paper [BS73] on the pricing and hedging of contingent claims. Since then their explicit pricing formula has become the market standard for pricing European stock op tions and related financial derivatives. In contrast to the equity market, no comparable model is accepted as standard for the interest-rate market as a whole. One of the reasons is that interest-rate derivatives usually depend on the change of a complete yield curve rather than only one single interest rate. This complicates the pricing of these products as well as the process of managing their market risk in an essential way. Consequently, a large number of interest-rate models have appeared in the literature using one or more factors to explain the potential changes of the yield curve. Beside the Black ([Bla76]) and the Heath-Jarrow-Morton model ([HJM92]) which are widely used in practice, the LIBOR and swap market models introduced by Brace, G~tarek, and Musiela [BGM97], Miltersen, Sandmann, and Son dermann [MSS97J, and Jamshidian [Jam98] are among the most promising ones.

Includes supplementary material: sn.pub/extras

Autorentext
Professor Dr. Rudi Zagst studierte Wirtschaftsmathematik an der Universität Ulm. Nach seiner Habilitation im Jahr 2000 an der Universität Ulm nahm Prof. Zagst im Jahr 2001 einen Ruf an die Technische Universität München als Professor für Finanzmathematik an und ist dort seit 2002 Leiter des HVB Stiftungsinstituts für Finanzmathematik. Im Jahr 2003 wurde er zum Ehrenvorsitzenden des Aufsichtsrates der risklab germany GmbH ernannt und erhielt im Jahr 2007 von der Zeitschrift "Unicum Beruf" die Auszeichnung zum "Professor des Jahres 2007" für sein Engagement um eine praxisnahe Ausbildung seiner Studenten.

Klappentext
The complexity of new financial products as well as the ever-increasing importance of derivative securities for financial risk and portfolio management have made mathematical pricing models and comprehensive risk management tools increasingly important.
This book adresses the needs of both researchers and practitioners. It combines a rigorous overview of the mathematics of financial markets with an insight into the practical application of these models to the risk and portfolio management of interest rate derivatives. It may also serve as a valuable textbook for graduate and PhD students in mathematics who want to get some knowledge about financial markets.
The first part of the book is an exposition of advanced stochastic calculus. It defines the theoretical framework for the pricing and hedging of contingent claims with a special focus on interest rate markets. The second part is a mathematically biased market-oriented description of the most famous interest rate models and a variety of interest rate derivatives. It covers a selection of short and long-term oriented risk measures as well as their application to the risk management of interest rate portfolios. Interesting and comprehensive case studies based on real market data are provided to illustrate the theoretical concepts and to illuminate their practical usefulness.

Inhalt
1 Introduction.- I Mathematical Finance Background.- 2 Stochastic Processes and Martingales.- 3 Financial Markets.- II Modelling and Pricing in Interest-Rate Markets.- 4 Interest-Rate Markets.- 5 Interest-Rate Derivatives.- III Measuring and Managing Interest-Rate Risk.- 6 Risk Measures.- 7 Risk Management.- 8 Appendix.- References.