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 engineering.

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 simulations. 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 financial instruments. 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

The Java-powered syllabus is structured to enable studies at two different levels.
  1. At a basic level, simple mathematics combined with market simulations provide a qualitative description of the payoff from European / American stock options, discount bonds and interest rate derivatives.
  2. 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 Vasicek model for bonds.
In all cases, the calculations can immediately be applied and compared with historical data 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.

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 learning environment. 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 application form (select "Blankett") before the course starts. Specific questions preferably by e-mail to André Jaun, NADA, KTH, 100 44 Stockholm, tel +4670 7971879

Course analysis

Here is a link to the analysis for the previous courses: 2005

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Content: André Jaun <>
Last modified 16 Dec 2005
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