2D4282, Financial Modeling: options, swaptions, derivatives
(distance-learning, 4 points / 6 ECTS)
Following a rather slow start in the 1970's when a few simple deals were
made only between specialists, increasingly sophisticated financial products
are now being developed and are commonly used by individuals everywhere:
employees get rewarded with the uncertain future earnings of their company,
flat owners insure themselves against the fluctuations in the interest rates
and investors try to limit their losses in falling markets.
Options come in different flavours to manage the investment risk in stock
and bond markets. Whether it is a plain vanilla European put option written
for an underlying share or a swaption giving its holder the right to swap
from a varying spot rate to a fixed interest rate, all these products
require a good understanding of what are the foundations of financial
Who is this course for?
Lifelong-learners with a scientific background and professionals from
financial institutions are most likely to enjoy the subject; a much
broader audience of non-specialists will however benefit from the
original manner advanced topics are here exposed with simple numerical
The material is organized in modules with different degrees of difficulty:
this allows business people who are unfamiliar with differential calculus
to learn intuitively from experiments and scientists to acquire a jargon
that is often assumed in the literature.
What are the course targets and the working strateagy?
The participant will be able to use historical data from the markets
and with the help of models calculate the fair price of a variety of
The course begins with a short review the basic securities that are
generally held in a portfolio and defines derivative contracts such
as options, futures and swaps together with the predetermined
cash-flows that are implied.
A discussion of the random nature of markets introduces students with
limited quantitative skills to the concept of numerical simulations.
At a more advanced level, graduates with an engineering background
will be able to reproduce the derivation and to implement their own
version of a model that awarded Black & Scholes in 1979 the
counterpart of the Nobel Prize in economics.
Every piece of theory is followed by a range of applications using
e.g. the virtual market applet VMARKET to get an intuitive
understanding for the payoff dynamics with a variety of options.
Choose your own level of difficulty
is structured to enable studies at two different levels.
In all cases, the calculations can immediately be applied and compared with
from the markets, using
time series models
(UWMA, EWMA, GARCH) to estimate the volatility and compare the
fair price of derivative contracts that have been calculated
with the price observed in the markets.
At a basic level, simple mathematics combined with market simulations
provide a qualitative description of the payoff from
interest rate derivatives.
- At an advanced level, a quantitative analysis of the random nature of
markets enables engineering students to derive and implement their own
financial models, including the
Black & Scholes
model for stock options and the
model for bonds.
Distance-learning and assessement
The course can be completed at a distance using a regular browser to
submit assignments with derivations and programs in a problem based
A strong emphasis is put on the problem based learning where the
participants analyze data, derive, implement, document and execute
their own models in a web browser everywhere on the Internet.
The first part of the course consists in a number of self-studies
and assignments with computer generated feed-back that can be
completed throughout the year (2 points / 3 ECTS).
The second part involves more complex problem based learning tasks
that are completed under the supervision of a human teacher when
the course officially takes place (2 points / 3 ECTS) and has to
be completed to finally qualify for a course certificate.
Basic calculus to complete the course at a basic level.
Differential calculus and elementary programing to complete the
course at an advanced level.
More info, contact and registration
More information and examples can directly be accessed from the course website
To register, Swedish students can simply
open an account
during the month before the course starts. Netuniversity and continued education
students from outside KTH have to fill-in the
(select "Blankett") before the course starts.
Specific questions preferably by e-mail to
André Jaun, NADA, KTH, 100 44 Stockholm,
tel +4670 7971879
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Last modified 16 Dec 2005
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