Minicourse on Quantitative Finance.

Date: September 26th and October 03, 10, 17, 24 (every friday), from 3 PM to 6PM.

Local: Praia de Botafogo, 190, Rio de Janeiro. Room 1332.


Margaret Armstrong and Alain Galli started the Quantitative Finance Group at the École des Mines de Paris in 2001. The group trains French engineers who want to be quants, traders & structurers in banks. The group’s research focuses on:

Modeling commodities (electricity, oil and gas, CO2 etc).
Modeling the structure of electricity markets, and the impact of the introduction of renewables (wind power) and electric vehicles on day-ahead electricity prices.
Evaluating and optimising of projects such as mines, oil fields and power plants that are subject to technical and financial uncertainty.
Modelling the term structure of interest rates.
Stochastic volatility models.
Dynamic hedging of physical commitments.
Copulas, especially Archimedean copulas.

Margaret Armstrong is a professor at the Cerna, Mines-Paristech. She has a masters in mathematical statistics from the University of Queensland, Australia, and a PhD in geostatistics from the École des Mines de Paris.

Alain GALLI is a professor at the Cerna, Mines-Paristech. He holds a PhD in mathematics from the University of Grenoble, France.


Week 1

Lecture 1: Basic theory on Geometric Brownian motion, Mean reverting processes
Lecture 2: Simulation procedures
Computer Session: Simulating a geometric Brownian motion

Week 2

Lecture 1: Options: puts & calls, European, American Asian, Black & Scholes formula
Lecture 2: First approach for pricing options: arbitrage, self-financing portfolios
Computer Session: Using Black & Scholes formula to price European options; zero cost collar

Week 3

Lecture 1: Second approach for pricing options: conditional expectation, Statement of Feynmann- Kac theorem
Lecture 2: Using binomial & trinomial trees to price American options
Computer Session: Constructing binomial trees for pricing options

Week 4

Lecture 1: Bonds, Interest rates, Foreign exchange, Term structure
Lecture 2: Stochastic processes for modelling interest rates
Computer Session: Comparing 3 ways to price European option (a) Simulating geometric
Brownian motion (b) Black & Scholes Formula (c) binomial tree

Week 5

Lecture 1: Commodities: spot prices futures, options. Applied to crude oil & to electricity markets
Lecture 2: Stochastic processes for commodities
Computer Session: Simulating commodity prices.

Examination procedure: computer exercise to be carried out in pairs and handed in 4 weeks end of course.