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Introduction to interest
rate modeling
1. Introduction to interest rates
Interest rate
behavior
Basic concepts
Interest rate markets
Historical and current data
Uses of interest rate models
2. Interest rates in history
Interest rates in monetary history
Characteristics of interest rate
behavior
3. Introduction to interest rate
modelling
Yield curve basics
Describing interest rate processes
Introduction to interest rate models
Categories of interest rate model
The role of the short rate
4. Interest rate models: theory
Summary of valuation
A theoretical market framework
Fundamentals of pricing
valuing by change of numeraire
Derivatives in the extended Vasicek
model
5. Basic modelling tools
Introduction to valuation
Introduction to estimation
Statistical tests
Yield curve stripping
The convexity adjustment
6. Densities and distributions
The density function
Kernel methods
Boundary behaviour
Interest rate models at extreme
values of interest rates
Tail distributions
Interest rate models
7. Affine models
Affine term structure models
Interpreting the state variables
Types of affine model
Examples of one-factor affine models
Examples of n-factor affine models
A general framework for affine models
8. Market models and the Heath,
Jarrow and Morton framework
Introduction to the Heath, Jarrow and
Morton model
Volatility functions in HJM
Market models
General market models
9. Other interest rate models
Consol models
Price kernel models
Positive interest rate models
Non-linear models
10. General formulations of
interest rate models
Jump processes
Random field models
A general model
Jump models
11. Economic models
Economics and interest rates
An economically motivated financial
model of interest rates
An IS-LM based model
IS-LM, hyperinflation and extended
Vasicek
The general equilibrium framework
Interpreting the price kernel
Valuation methods
12. Finite difference methods
The Feynman-Kac Equation
Discretising the PDE
Simplifying the PDE
Explicit methods
Implicit methods
The Crank-Nicolson method
Comparison of methods
Implicit boundary conditions
Fitting to an initial term structure
Finite difference methods in N
dimensions
Operator splitting
A two-dimensional PDE
Solving a PDDE
13. Valuation: the Monte Carlo
method
The basic Monte Carlo method
Speed-up methods
Sampling issues
Simulation methods for HJM models
14. Lattice methods
Introduction to lattice methods
Issues in constructing a lattice
Examples of lattice methods
Calibration to market prices
The explicit finite difference method
Lattices and the Monte Carlo method
Non-recombining lattices
Calibration and
estimation
15. Modelling the yield curve
Stripping the yield curve
Fitting using
parameterized curves
Fitting the yield curve using splines
Nelson and Siegel curves
Comparison of families of curves
Kernel methods of yield curve
estimations
LP and regression methods
16. Principal components analysis
Volatility structures
Identifying empirical volatility
factors
Calibrating whole yield curve methods
Processes on manifolds
Analysis of dynamical systems
Principal
components analysis
Volatility structures
Identifying empirical volatility
factors
Calibrating whole yield curve methods
Processes on manifolds
Analysis of dynamical systems
17. Estimation methods: GMM and ML
GMM estimation
Implementation issues
The efficient method of moments (EMM)
Maximum likelihood methods
Hierarchy of procedures
18. Further estimation methods
Filtering approaches to estimation
The extended Kalman Filter
GARCH models
Extensions of GARCH
Interest rate models and GARCH
Artificial neural nets (ANNs)
19. Interest rates and implied
pricing
Problems with interest rate models
Key relationships
The interest rate case
The implied pricing method
Regularization functions
Patching tail |
the Vasicek model with time-varying mean;