Interest-Rate Models and the Pricing of Derivatives:
Practical implementation and calibration methods
The outline for the course is to develop an understanding of
multi-factor models that can be applied to the valuation of
interest-rate derivatives, such as European-style and Bermudan-style
swaptions. The course will begin by reviewing various approaches
that have been suggested and used and will then concentrate
on the practical implementation of the LIBOR Market Model (LMM).
A new approach to building a two-factor, recombining LMM will
be explained and illustrated. This approach uses the Ho, Stapleton
and Subrahmanyam recombining binomial tree method. Methods of
calibrating the model to market prices of caps and swaptions
will be discussed.
All teaching is delivered by Professor Richard Stapleton.
- Review of interest-rate models: Purpose of the models,
Spot-rate vs. forward-rate models, single-factor vs. multi-factor
models. Standard models for valuation of caps, floors and
swaptions. The Black model for pricing LIBOR futures options.
- Development and proof of The LIBOR market model (Brace,
Gatarek, Musiela model (BGM)). Main features of the LMM:
consistency with the Black model for caplets.The forward
rate drift in the LMM.
- Inputs for the LMM. Steps required for building a one-factor
LMM. Building a spreadsheet version of the LMM. The difference
between the LMM prices and BK prices for caplets and floorlets.
Exercise: build a spreadsheet version of a one-factor two-factor
model, 'bushy tree' case.
- Calibrating and implementing a 2-factor LMM. Calibration
to forward rates, caplet volatilities. Fitting the correlation
of forward rates. Calibrating to swaption volatilities.Pricing
of Bermudan-style swaptions using the LMM. A recombining
binomial version of the 2-factor LMM. A comparison with
the 2-factor spot rate approaches of Hull-White and Peterson,
Stapleton and Subrahmanyam.
If you would like to register an interest in participating in
any future courses on the Libor Market Model, or if you would
like us to perform a course on your behalf, then please register
your interest here.