Term Structure Models A Graduate Course 1st edition by Damir Filipovic – Ebook PDF Instant Download/Delivery: 364226915X, 978-3642269158
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ISBN 10: 364226915X
ISBN 13: 978-3642269158
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:
Interest Rates and Related Contracts
Zero-Coupon Bonds
Interest Rates
Market Example: LIBOR
Simple vs. Continuous Compounding
Forward vs. Future Rates
Money-Market Account and Short Rates
Proxies for the Short Rate
Coupon Bonds, Swaps and Yields
Fixed Coupon Bonds
Floating Rate Notes
Interest Rate Swaps
Yield and Duration
Yield-to-Maturity
Duration and Convexity
Market Conventions
Day-Count Conventions
Coupon Bonds
Accrued Interest, Clean Price and Dirty Price
Yield-to-Maturity
Caps and Floors
Caps
Floors
Caps, Floors and Swaps
Black’s Formula
Swaptions
Black’s Formula
Exercises
Notes
Estimating the Term-Structure
A Bootstrapping Example
Non-parametric Estimation Methods
Bond Markets
Money Markets
Problems
Parametric Estimation Methods
Estimating the Discount Function with Cubic B-splines
Smoothing Splines
Exponential-Polynomial Families
Principal Component Analysis
Principal Components of a Random Vector
Sample Principle Components
PCA of the Forward Curve
Correlation
Exercises
Notes
Arbitrage Theory
Stochastic Calculus
Stochastic Integration
Quadratic Variation and Covariation
Itô’s Formula
Stochastic Differential Equations
Stochastic Exponential
Financial Market
Self-Financing Portfolios
Numeraires
Arbitrage and Martingale Measures
Martingale Measures
Market Price of Risk
Admissible Strategies
The First Fundamental Theorem of Asset Pricing
Hedging and Pricing
Complete Markets
Arbitrage Pricing
Exercises
Notes
Short-Rate Models
Generalities
Diffusion Short-Rate Models
Examples
Inverting the Forward Curve
Affine Term-Structures
Some Standard Models
Vasicek Model
CIR Model
Dothan Model
Ho-Lee Model
Hull-White Model
Exercises
Notes
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
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