CEMLA Course: Financial Mathematics

November 21 - 25, 2022


Monday, November 21
Brownian processes and Itô calculus

Random variables, definition of a Brownian process, properties of the Brownian process, multivariate Brownian process, simulation of a Brownian process in Python. Definition of the Itô Integral, properties of the Itô Integral, Itô-Doeblin formula, multivariate Itô-Doeblin formula, and applications.

Tuesday, November 22
Black and Scholes valuation, and risk neutral valuation

Stochastic discount factor, the Black and Scholes economy, Black and Scholes extensions. Change of probability measure (Girsanov's theorem), risk neutral valuation and its relationship with the stochastic discount factor, and applications.

Wednesday, November 23
Numerical methods and implementation

Monte Carlo simulation, explicit finite differences, implicit finite differences in Python. Applications to option pricing with mean-reversion and stochastic volatility.

Thursday, November 24
Asset pricing models and applications

Static and dynamic models for bonds, futures, options, options on bonds and swaps. Estimation of linear models in Python. Multifactorial models applied to commodity futures, swaps and options on inflation, bonds with near-zero rates.

Friday, November 25
Kolmogorov equations and dynamic programming

Transition probabilities, Kolmogorov forward equations, Kolmogorov backward equations, application to HACT models. Finite horizon dynamic programming, Infinite horizon dynamic programming, jumps and dynamic programming with regime shifts, application to HACT models. Dynamic programming and numerical methods.

Jaime Casassus

Jaime Casassus works as an Associate Professor at the Institute of Economics of the Pontificia Universidad Católica de Chile. Jaime holds a Ph.D. in Finance from Carnegie Mellon University, a B.S. in Civil Industrial Engineering and a M.S. in Industrial Engineering from the Pontificia Universidad Católica de Chile. He has also been Managing Editor for Quantitative Finance, Associate Editor for the Journal of Commodity Markets, Visiting Professor at the University of California, Berkeley and Member of the Finance Committee that advises the Chilean Ministry of Finance on the investment policy of its sovereign wealth funds. Jaime has publications in Journal of Banking & Finance, Journal of Futures Markets, Review of Financial Studies, European Financial Management, Journal of Finance, among other journals.