In order to pass the course the student should be able to
explain the principles for pricing financial derivatives;
explain the principles of simulation based on Monte Carlo;
explain Brownian motion and geometric Brownian motion in detail;
apply methods for variance reduction in the context of pricing financial derivatives;
explain the principles of quasi Monte Carlo and apply the method of quasi Monte Carlo in the context of pricing financial derivatives;
apply methods of Monte Carlo to calculate sensitivity parameters for financial derivatives;
apply methods of Monte Carlo for pricing of financial derivatives of American type.
Principles of Monte Carlo, principles of pricing financial derivatives, random number generation, general sampling methods, normal random variables and vectors, Brownian motion, geometric Brownian motion, variance reduction techniques, control variates, antithetic variates, stratified sampling, importance sampling, quasi Monte Carlo, the principles of quasi Monte Carlo, Halton sequences, Faure sequences, Sobol sequences, estimation of sensitivities, finite difference approximations, pathwise derivatives estimates, the likelihood ratio method, pricing American options, parametric approximations, random tree methods, regression based methods, the method based on duality.
Lectures and computer laboratories.
Compulsory assignments in accordance with instructions at course start.
week 30, 2012
Monte Carlo methods in financial engineering