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Financial Modeling: Options, Swaps and Derivatives

André Jaun, NADA, Royal Institute of Technology, Stockholm

Register now for the Netuniversity edition (Sep 19 - Dec 15, 2005)

This is the web edition of the distance learning courses taught at the Royal Institute of Technology in Stockholm (KTH course 2D5244, 4 points), the University of Adelaide (Masters in Applied Finance programme), the Swedish Netuniversity (KTH course 2D4282, 4 points) and independent learners from outside Sweden. The target is to familiarize the participants with the methodology used in financial engineering to manage the investment risks in stock and bond markets.
The material has been designed so that it can be studied at different levels depending on the mathematical background and the ambition of every participant: with little algebra, practitionners get a practical understanding of the option payoff dynamics using virtual market experiments in a java-powered web browser. At a more advanced level, graduates from quantitative fields learn how to use stochastic calculus to formulate financial models and to implement numerical solutions in the VMARKET applet: be patient, it takes about 15 secs to load with a 56K modem...

VMARKET applet  press START/STOP to simulate the price of an American vanilla put option up to half a year before it expires using finite elements. The black (alt. grey) line shows the present (alt. terminal) value of the option V(S,t) for a whole range of underlying prices 0 < S < 16. Click in the plot area to measure the value of the option.

Hedging strategies involving shares, bonds and their derivatives are discussed, starting from no arbitrage arguments to derive PDEs such as the celebrated Black-Scholes equation. Solutions obtained using finite differences, finite elements and Monte-Carlo methods are compared with each other and provide the background to implement more sophisticated models. Assignments are an essential part of the learning process: they are submitted from the web browser and automatically compiled into web pages where the students explain with words, equations and programs how to derive, implement and run their own numerical schemes.


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