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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 javapowered 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...
Hedging strategies involving shares, bonds and their derivatives are discussed, starting from no arbitrage arguments to derive PDEs such as the celebrated BlackScholes equation. Solutions obtained using finite differences, finite elements and MonteCarlo 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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