Term Structure Models A Graduate Course 1st edition by Damir Filipovic – Ebook PDF Instant Download/Delivery: 3540097260, 978-3540097266
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ISBN 10: 3540097260
ISBN 13: 978-3540097266
Author: Damir Filipovic
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.
Term Structure Models A Graduate Course 1st Table of contents:
- Heath-Jarrow-Morton (HJM) Methodology
- Forward Curve Movements
- Absence of Arbitrage
- Short-Rate Dynamics
- HJM Models
- Proportional Volatility
- Fubini’s Theorem
- Exercises
- Notes
- Forward Measures
- T-Bond as Numeraire
- Bond Option Pricing
- Example: Vasicek Short-Rate Model
- Black-Scholes Model with Gaussian Interest Rates
- Example: Black-Scholes-Vasicek Model
- Exercises
- Notes
- Forwards and Futures
- Forward Contracts
- Futures Contracts
- Interest Rate Futures
- Forward vs. Futures in a Gaussian Setup
- Exercises
- Notes
- Consistent Term-Structure Parametrizations
- Multi-factor Models
- Consistency Condition
- Affine Term-Structures
- Polynomial Term-Structures
- Special Case: m=1
- General Case: m>=1
- Exponential-Polynomial Families
- Nelson-Siegel Family
- Svensson Family
- Exercises
- Notes
- Affine Processes
- Definition and Characterization of Affine Processes
- Canonical State Space
- Discounting and Pricing in Affine Models
- Examples of Fourier Decompositions
- Bond Option Pricing in Affine Models
- Example: Vasicek Short-Rate Model
- Example: CIR Short-Rate Model
- Heston Stochastic Volatility Model
- Affine Transformations and Canonical Representation
- Existence and Uniqueness of Affine Processes
- On the Regularity of Characteristic Functions
- Auxiliary Results for Differential Equations
- Some Invariance Results
- Some Results on Riccati Equations
- Proof of Theorem 10.3
- Exercises
- Notes
- Market Models
- Heuristic Derivation
- LIBOR Market Model
- LIBOR Dynamics Under Different Measures
- Implied Bond Market
- Implied Money-Market Account
- Swaption Pricing
- Forward Swap Measure
- Analytic Approximations
- Monte Carlo Simulation of the LIBOR Market Model
- Volatility Structure and Calibration
- Principal Component Analysis
- Calibration to Market Quotes
- Continuous-Tenor Case
- Exercises
- Notes
- Default Risk
- Default and Transition Probabilities
- Structural Approach
- Intensity-Based Approach
- Construction of Doubly Stochastic Intensity-Based Models
- Computation of Default Probabilities
- Pricing Default Risk
- Zero Recovery
- Partial Recovery at Maturity
- Partial Recovery at Default
- Measure Change
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