Students are expected to gain, beside the theoretical concepts, programming skills that are related to option pricing as well as optimization. The outcomes are to be able to apply the numerical methods on the following: 

• Fixed-income securities, basic portfolio optimization, binomial method for options;
• Ito process and its applications in stock market, Black-Scholes equation and its solution;
• random numbers, transformation of random numbers and generating normal variates,
• Monte Carlo integration, pricing options by Monte Carlo simulation, variance reduction techniques, quasi-random numbers and quasi-Monte Carlo simulation;
• finite difference methods, explicit and implicit finite difference schemes, Crank-Nicolson method, free-boundary value problems for American options.