The scope of this course is to provide students with basic tools for financial computing, such as, pricing derivatives under standard option pricing models such as binomial, Black-Scholes and its extensions via Monte Carlo simulation.
Prerequisiti
Solid knowledge in Mathematics (including calculus, linear algebra, probability, stochastic processes) and Statistics (descriptive statistics, regression analysis), basic Programming skills (Matlab, R or Python), basic knowledge of Quantitative Finance (Binomial and Black-Scholes option pricing models)
Metodi didattici
Classroom lectures. Matlab laboratory. Homework exercises, code development, and data analysis
Verifica Apprendimento
Oral exams/assignement.
Testi
Didactic materials will be supplied by the instructor. They integrate from multiple sources:
1) Bjork, Arbitrage Theory in Continuous Time 2) Fusai&Roncoroni, Implementing Models in Quantitative Finance, 2008 3) Glasserman, Monte Carlo Methods in Financial Engineering, 2004 4) Seydel, Tools for Computational Finance
Contenuti
1) Monte Carlo methods (Central limit theorem, random sampling schemes) 2) Binomial model: recall of the theory, Matlab implementation, examples on real data 3) Black-Scholes model: pricing formula, greeks and sensitivities, European options’ portfolio management (with Matlab) 4) Black-Scholes model: path dependent options and variance reduction techniques (with Matlab) 5) Simulation of stochastic differential equations (exact sampling and approximate dynamics) (with Matlab) 6) Beyond Black-Scholes: jump diffusion processes and stochastic volatility (Heston model) (with Matlab examples)
