Interest Rate Models  Advanced Pricing and Risk Management
Duration: 2 days
 The Term Structure of Interest Rates and Volatility
 Equilibrium and NoArbitrage Models
 The BDT and the HullWhite Models
 The Libor Market (BGM) Model
 MultiCurve Libor Market Models
 Stochastic Volatility Models
 Using Interest Rate Models in Risk Management
The objective of this advancedlevel seminar is to give you a good understanding of modern interest
rate models and their uses in option pricing and risk management.
We first present and explain important concepts such as the term structure of interest rates and the
term structure of volatility. We then take a closer look at various processes for interest rate
evolvement over time, and we explain how interest rate volatility can be modelled into these
processes.
Next, we present and explain a number of “classical” models for interest rate processes, including
“Equilibrium” models such as the RendlemanBarter and CoxIngersollRoss and “Noarbitrage” models 
with and without mean reversion features. This class of models includes singlefactor models such as
the HoLee, Vasicek, HullWhite, BlackDermanToy as well as twofactor models such as
LongstaffSchwartz. We also present the popular “Libor Market”, or BGM (BraceGatarekMuselia), model,
which is widely used by practitioners. We discuss the important characteristics and parameters of these
models, and we demonstrate how they can be constructed, calibrated and implemented in practice using
treebuilding procedures and Monte Carlo simulation.
Further, we present and explain a doublecurve framework, adopted by the market after the liquidity
crisis started in summer 2007. We revisit the problem of pricing and hedging plain vanilla single
currency interest rate derivatives using different yield curves for market coherent estimation of
discount factors and forward rates with different underlying rate tenors. We also derive the no
arbitrage double curve marketlike formulas for basic plain vanilla interest rate derivatives and show
how they can be used for pricing of FRA, swaps, cap/floors and swaptions etc.
Further, we present models for stochastic volatility, exemplified by the widely used Heston Model
today. We motivate the uses of such models, and we show how the model is computationally validated,
calibrated and applied in the pricing of standard and more exotic interest rate options.
Finally, we look at how interest rate models can be used for various risk management purposes,
including calculating key ratios and estimating return distributions for “ValueatRisk” calculation.
Day One
09.00  09.15 Welcome and Introduction
09.15  12.00 Introduction to Interest Rate Modelling
 Interest Rates and their Behavior
 The Term Structure of Interest Rates and Volatility

Features of Interest Rate Models
 Noarbitrage
 Mean reversion
 Spot or forward rates
 Stochastic volatility
 New Challenges in Interest Rate Modelling
Equilibrium Models
 Rendleman and Barter

Vasicek
 Mean reversion in the Vasicek model
 Term structures in the Vasicek Model

Cox, Ingersoll, & Ross (CIR)
 General form of CIR
 Term structures in the CIR model
 Examples and Exercises
12.00  13.00 Lunch
13.00  16.30 Classical Noarbitrage Models  Single Curve Environment

The BDT Model
 General form
 Deriving the model from zero curve and volatility structure

The HullWhite Model
 A general treebuilding procedure
 The Swap Market Model
 The Libor Market (BGM) Model
 Using Monte Carlo Simulation with Interest Rate Models

SingleCurve Pricing & Hedging InterestRate Derivatives – Examples
 Swaps
 Caps, floors, swaptions
 Exotic interest rate options
 Structured interest rate products
 Exercises
Day Two
09.00  09.15 Recap
09.15  12.00 Modern Libor Market Models
 From Single to DoubleCurve Paradigm

DoubleCurve Framework, No Arbitrage and Basis Adjustment
 General Assumptions
 Pricing Procedure
 No Arbitrage Revisited and Basis Adjustment
 The Double Curve Libor Market Model

ForeignCurrency Analogy and Quanto Adjustment
 The DoubleCurve Lognormal LMM

ForeignCurrency Analogy and Quanto Adjustment

DoubleCurve Pricing & Hedging Interest Rate Derivatives (Examples)
 Swaps
 Caps, floors, swaptions
 Exotic interest rate options
 Examples and Exercises
12.00  13.00 Lunch
13.00  16.30 Stochastic Volatility Models
 The World of Stochastic Volatility

The Heston Model
 Motivation and parameters
 Computational valuation
 Calibration
 Generating volatility surfaces and skews
 Pricing Options Using Stochastic Volatility Models
 Examples and Exercises
Using Interest Rate Models in Risk Management
 Hedging Instruments and Hedging Process
 Calculating Key Ratios and Hedge Ratios
 Generating Return Distributions and Calculating “ValueatRisk”
Evaluation and Termination of the Seminar
