Disponible en Español

CEMLA Course: Financial Mathematics

November 11 - 15, 2024
Videoconference

CEMLA organized the CEMLA Course: Financial Mathematics, which was held virtually from November 11 to 15, 2024. The course featured the participation of 106 representatives from 25 member institutions, associates, and collaborators of CEMLA, spanning 22 countries. During the event, key stochastic and numerical models used in derivatives and bond markets were presented.

In the first session, anecdotes about the use of financial instruments were shared, along with a brief overview of the development of financial mathematics. Stochastic calculus was introduced to model market uncertainty, starting with random walks, transitioning to Brownian motion as a continuous limit, and culminating in stochastic differential equations and Itô’s lemma.

The second session focused on the Feynman-Kac theorem, which connects stochastic differential equations with the Cauchy problem in partial differential equations, leading to the derivation of the Black-Scholes formula. The session concluded with practical applications for pricing vanilla options in real markets, comparing theoretical results with observed values.

In the third session, the Put-Call parity relationship and other parity relationships were explained. Additionally, position hedging using replicating portfolios was analyzed, employing the Black-Scholes formula for approximations.

The fourth session concentrated on the binomial model to determine periodic rebalancing of hedging portfolios. Monte Carlo simulations for option pricing were also explored. The day ended with the introduction of investment strategies focused on trends and volatility.

Finally, the fifth session formalized the use of these strategies. The course concluded with an introduction to fixed income theory, modeling zero-coupon bonds from three perspectives: short-term interest rates, forward rates, and direct bond pricing. Notable models such as Vasicek, Cox-Ingersoll-Ross, Dothan, and Hull-White were highlighted.