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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.

Quantitative methods (economics) --- financiële analyse --- toegepaste wiskunde --- Operational research. Game theory --- speltheorie --- kansrekening --- Financial analysis --- Mathematics --- stochastische analyse --- EPUB-LIV-FT LIVMATHE LIVSTATI SPRINGER-B --- Money market. Capital market --- Finanzmathematik. --- Fixed-income securities --- Interest rate risk. --- Interest rates --- Options (Finance). --- Zinsstrukturtheorie. --- Valuation --- Mathematical models. --- Interest rate risk --- Options (Finance) --- 305.7 --- 333.642 --- AA / International- internationaal --- Call options --- Calls (Finance) --- Listed options --- Options exchange --- Options market --- Options trading --- Put and call transactions --- Put options --- Puts (Finance) --- Derivative securities --- Investments --- Risk --- Fixed-income investments --- Investments, Fixed-income --- Securities, Fixed-income --- Securities --- Valuation&delete& --- Mathematical models --- Econometrie van het gedrag van de financiële tussenpersonen. Monetaire econometrische modellen. Monetaire agregaten. vraag voor geld. Krediet. Rente --- Termijn. Financial futures --- Law and legislation

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Quantitative methods (economics) --- Operational research. Game theory --- Mathematics --- Financial analysis --- toegepaste wiskunde --- stochastische analyse --- speltheorie --- financiële analyse --- kansrekening

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The book is written for a reader with knowledge in mathematical finance (in particular interest rate theory) and elementary stochastic analysis, such as provided by Revuz and Yor (Continuous Martingales and Brownian Motion, Springer 1991). It gives a short introduction both to interest rate theory and to stochastic equations in infinite dimension. The main topic is the Heath-Jarrow-Morton (HJM) methodology for the modelling of interest rates. Experts in SDE in infinite dimension with interest in applications will find here the rigorous derivation of the popular "Musiela equation" (referred to in the book as HJMM equation). The convenient interpretation of the classical HJM set-up (with all the no-arbitrage considerations) within the semigroup framework of Da Prato and Zabczyk (Stochastic Equations in Infinite Dimensions) is provided. One of the principal objectives of the author is the characterization of finite-dimensional invariant manifolds, an issue that turns out to be vital for applications. Finally, general stochastic viability and invariance results, which can (and hopefully will) be applied directly to other fields, are described.

Applied mathematics. --- Engineering mathematics. --- Finance. --- Economics, Mathematical. --- Probabilities. --- Applications of Mathematics. --- Finance, general. --- Quantitative Finance. --- Probability Theory and Stochastic Processes.

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We propose a new framework to explain the factor structure in the full cross section of Treasury bond returns. Our method unifies non-parametric curve estimation with cross-sectional factor modeling. We identify smoothness as a fundamental principle of the term structure of returns. Our approach implies investable factors, which correspond to the optimal spanning basis functions in decreasing order of smoothness. Our factors explain the slope and curvature shapes frequently encountered in PCA. In a comprehensive empirical study, we show that the first four factors explain the time-series variation and risk premia of the term structure of excess returns. Cash flows are covariances as the exposure of bonds to factors is fully explained by cash flow information. We identify a state-dependent complexity premium. The fourth factor, which captures complex shapes of the term structure premium, substantially reduces pricing errors and pays off during recessions.