This graduate textbook provides an introduction to the mathematics of term structure models in continuous time. The focus is on a mathematically straightforward but rigorous development of the theory.

Changing interest rates constitute one of the major risk sources for banks, insurance companies, and other financial institutions. Modeling the term-structure movements of interest rates is a challenging task. This volume gives an introduction to the mathematics of term-structure models in continuous time. It includes practical aspects for fixed-income markets such as day-count conventions, duration of coupon-paying bonds and yield curve construction; arbitrage theory; short-rate models; the Heath-Jarrow-Morton methodology; consistent term-structure parametrizations; affine diffusion processes and option pricing with Fourier transform; LIBOR market models; and credit risk.

The focus is on a mathematically straightforward but rigorous development of the theory. Students, researchers and practitioners will find this volume very useful. Each chapter ends with a set of exercises, that provides source for homework and exam questions. Readers are expected to be familiar with elementary Itô calculus, basic probability theory, and real and complex analysis.

First graduate textbook that covers topics ranging from fixed-income market conventions, the estimation and statistics (PCA) of the yield curve, arbitrage theory, short-rate models, the Heath-Jarrow-Morton methodology (including a derivation of Fubini's Theorem for stochastic integrals), LIBOR market models, credit-risk, and the special chapters on consistent term structure parameterizations and affine processes All chapters end with a set of exercises, which provides the source for homework and exam questions

Autorentext

Damir Filipovic is head of the Vienna Institute of Finance, a research institution in the field of Mathematical Finance, funded by the Vienna Science and Technology Fund (WWTF), and founded and co-funded by the University of Vienna and the Vienna University of Economics and Business Administration. Prior to this position he held the Chair of Financial and Insurance Mathematics at the University of Munich, and he was Assistant Professor at Princeton University. Moreover, he worked for the Swiss Federal Office of Private Insurance, where he co-developed the Swiss Solvency Test (SST) - a risk based solvency assessment for insurance undertakings - which was enacted in 2006. He also held visiting positions at ETH Zurich, Columbia University, Stanford University, and the Vienna University of Technology.

Inhalt
Interest Rates and Related Contracts.- Estimating the Term-Structure.- Arbitrage Theory.- Short-Rate Models.- HeathJarrowMorton (HJM) Methodology.- Forward Measures.- Forwards and Futures.- Consistent Term-Structure Parametrizations.- Affine Processes.- Market Models.- Default Risk.