The purpose 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
Next, we present and
explain a number of models for
interest rate processes, including "Equilibrium"
models such as the Rendleman-Barter and Cox-Ingersoll-Ross and
"No-arbitrage" models - with and without mean reversion features.
This class of models includes single-factor models such as the
Ho-Lee, Vasicek, Hull-White,
Black-Derman-Toy as well as multi-factors models such as
Longstaff-Schwartz. We also present the popular "Libor
Market", or BGM (Brace-Gatarek-Muselia) 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
path-dependent option structures (using Monte Carlo simulation).