Interest Rate Models

Learn how to develop, calibrate and validate models in order to eliminate model risk and guarantee robustness. More importantly, learn the practicalities of pricing, hedging and position taking, using interest rate models, as well as how to avoid potential problems

Course Highlights

“The course introduces you to most advanced tools and at the same time gives you an overall view of standard techniques for modelling interest rates”

R.Z., Banca di Roma

This training course covers the mathematical concepts underlying a broad spectrum of interest rate models, including:

Modelling in the bond markets and the money markets
Hull and White, BDT and many other models
Market models: Choosing volatilities and correlations
Implementation using Monte Carlo and Lattice
Modelling credit risk

For details of the course trainer, please download the course brochure

Booking Information

Dates	Prices	Book This Course	Discount
01 - 03 Dec 2010	£ 2199		-
06 - 08 Jun 2011	£ 2199		-

Course Programme

“The course introduces you to most advanced tools and at the same time gives you an overall view of standard techniques for modelling interest rates”

R.Z., Banca di Roma

Top notch instructor, deep knowledge of subject, up-to-date with research

A.E., Senior Economist, National Bank of Greece

“The speaker introduced a broad range of models and techniques. Improved my knowledge a lot”

K.B., Heleba

Introducing the mathematical concepts and preliminaries underlying interest rate models

The jargon of valuation: describing interest rate processes
Numeraires, equivalent Martingale measures and risk-neutral valuation
Feynman-Kac, Girsanov, Kolmogorov
The forward measure

Fitting the yield curve

The choice of parametric or non-parametric curve fitting
Spline methods; B-spline, smoothing splines
Kernel methods
Nelson and Siegel curves

Workshop: Fitting the yield curve
Evaluating the success in practice of curve fitting techniques on yield curve data

Describing the basic models

Affine term structure models:
- Vasicek; Cox, Ingersoll and Ross; Longstaff and Schwartz; etc.
The Heath, Jarrow and Morton framework:
- The no-arbitrage conditions
- Pricing in the HJM framework

Workshop: Pitfalls with basic models
In this workshop the use and limitations of the basic models are explored, leading on to the more advanced models considered later in the course

Calibrating models to fit the interest rate curve

Calibration using historical or cross-sectional data
Problems with naive methods
Obtaining model parameters
The general method of moments, maximum likelihood methods
Non-parametric methods: using kernel functions to estimate probabilities and moments

Valuing and hedging interest rate products: Monte Carlo methods

The basic method
Basic speed-up methods: antithetic variates, control variates
Stratified sampling and the Brownian bridge
Quasi-random numbers
Spectral Decomposition and Moment matching methods
Valuing American and Bermudan style interest rate derivative

Workshop: Monte Carlo methods
Using Monte Carlo methods to value interest rate instruments. Comparison of various speed-up methods implemented in Visual Basic

Valuing and hedging interest rate products: Finite different methods

Explicit, implicit and Crank-Nicolson schemes
Specifying boundary conditions

Valuing and hedging interest rate products: Lattice methods

Lattice methods: binomial or trinomial methods?
Exploration of lattice methods: Hull and White; Black, Derman and Toy; Schmidt
Pricing on a lattice: Ritchken and Sankarasubramanian
Obtaining hedge ratios
Fitting to the initial yield curve
Fitting to initial volatilities

Workshop: Lattice methods
You will participate in hands-on exercises in order to grasp the practicalities of using alternative lattice methods for valuing and hedging interest rate products

Market models

Market models: calibrating to market prices
Recovering Blacks' formulae
General market models
Implementing market models: overview and examples
The BGM model: relationship of market models to the HJM framework

Workshop: Market models
Delegates are given hands-on experience with market models, using them to calibrate to prices of caps and swaptions and fitting to a volatility smile

Understanding volatility structures

Calibrating HJM and market models
Obtaining volatility curves: fitting theoretical curves
Extracting volatility curves from the data
Principal components analysis and historical data
Implied covariance matrices: calibrating to market prices
Kennedy's Random field approach: better calibration of HJM models

Credit risk

The issue of default risk and default correlation
Structural and reduced form models
Copula methods for modelling default risk
A credit rating model of credit risk
Pricing credit derivatives

Workshop: Credit risk
Using Visual Basic implementations, delegates assess the credit risk of simple portfolios and see how the models can be applied to value credit derivatives