Term Structure Modelling and Interest Rate Option Pricing
Duration: 3 days
 Term Structure of Interest Rates
 Modelling Volatility Using GARCH and EWMA
 Equilibrium and NoArbitrage Models
 Incorporating Mean Reversion
 Constructing and Calibrating Interest Rate Trees
 Libor Market Model
 Pricing and Using Interest Rate Options
 Pricing Callable and Defaultable Bonds
The objective of this advanced level seminar is to give you a good understanding of 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 at closer look at various processes for interest rate evolvement over time, and we explain
how interest rate volatility can be modelled in these processes using models such as
GARCH and EWMA (Exponentially Weighted Moving Average). We also explain various approaches to
modelling, including the use of partial differential equations and “Martingales”.
Next, we present and explain a number of 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 multifactors 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 implemented in
practice.
Finally, we explain and illustrate how these models can be used for pricing and risk assessment
of interest rate options such as Caps, Floors, Swaptions, Delivery Options, Prepayment Options
and Defaultable Bonds. We also demonstrate the pricing and hedging of more advanced
structures such as “Constant Maturity Swaps” (convexity adjustment) and of pathdependent
option structures (using Monte Carlo simulation).
Day One
09.00  09.15 Welcome and Introduction
09.15  12.00 The Term Structure of Interest Rates
 The Term Structure and its Applications
 Factors Explaining Shape of Term Structure
 Brief Review of Term Structure Estimation Techniques
Modelling Volatility
 Definition of Volatility
 Types of Volatility
 Standard Approach to Estimating Volatility
 Check for Normality of the Returns
 Possible Explanations for the Fat Tails

Moving Averages
 Simple moving average
 EWMA
 Attractions of EWMA
 The EWMA as special case of the GARCH process
 Examples and exercises
12.00  13.00 Lunch
13.00  16.30 Modelling Volatility (Continued)

GARCH Modelling
 Introduction
 General model appearance
 Conditional and unconditional variance
 GARCH (1,1)
 Higher order GARCH

Implementing GARCH
 Variance targeting
 Maximum Likelihood Methods
 Forecasting Future Volatility
 Volatility Term Structures
 Combining GARCH with EVTtheory to Capture Fat Tails
 Modelling Correlations
 Volatility Clustering and Correlations
 Examples and exercises
Day Two
09.00  09.15 Recap
09.15  12.00 Term Structure Models
 Introduction to Interest Rate Models

Features of Interest Rate Models
 One or two factors
 Noarbitrage
 Mean reversion
 Spot or forward rates

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
 Mean reversion in the CIR model
 Term structures in the CIR model
 Disadvantage of equilibrium models
 Examples and Exercises
12.00  13.00 Lunch
13.00  16.30 Term Structure Models (Continued)
 Noarbitrage Models
 Markov vs. nonMarkov Models
 The Ho and Lee Model

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

The HullWhite Model
 A general treebuilding procedure
 Building the tree – stage one
 Calculating branching probabilities
 Building the tree – stage two
 The Libor Market (BGM) Model
 Using Monte Carlo Simulation with Interest Rate Models
 Examples and Exercises
Day Three
09.00  09.15 Recap
09.15  12.00 Pricing Interest Rate Options Using Term Structure Models
 Pricing Options on Zero Coupon Bonds
 Pricing Options on CouponBearing Bonds

Pricing Libor Options
 Interest Rate Guarantees
 Caps and Floors
 Swaptions
 “Cancellation Swaps“

Pricing Structured Interest Rate Products
 “Capped FRNs“
 “Inverse Floaters“
 “Fairway Bonds“

Pricing Exotic Structures
 Captions, floptions and other compounds
 Ratchet caps, sticky caps, and flexi caps etc.
 Examples and Exercises
12.00  13.00 Lunch
13.00  16.00 Pricing Callable and Defaultable Bonds
 General Characteristics of Callable Bonds

Pricing Callable Bonds
 Singlecall and multiplecall bonds
 Prepayment Models
 Integrating Prepayment Models into an Interest Rate Model

Optionadjusted analysis
 OAS, OAY, Optionadjusted duration, ZSpread

Pricing Mortgage Bonds

Pricing Defaultable Bonds
 Incorporating credit spreads into term structure models
 Examples and Exercises
Evaluation and Termination of the Seminar
