Financial Mathematics


This curricular unit has as i ts main objective that students acquire knowledge about the fundamentals of mathematical models for the financial markets and for a wide variety of derivative financial products. It is intended that students understand the dynamics of the prices of financial assets and to be able to respond to problems of derivatives pricing, optimal portfolio choices and hedging.

General characterization





Responsible teacher

Marta Cristina Vieira Faias Mateus


Weekly - 4

Total - 56

Teaching language



Basic knowledge of Mathematical Analysis and Probability and Statistics.


● Benninga, S., Financial Modeling, MIT Press 2008.
● Bingham, N. H.; Kiesel, R., Risk-Neutral Valuation – Pricing and Hedging of Financial Derivatives, Springer, 2004.
● Bodie, Z., Kane, A. and Marcus, A., Essentials of Investments, McGraw-Hill, 2008.
● Hoek, J., Elliot, R. Binomial Models in Finance, Springer, 2006.
● Hull, J., Options Futures and Other Derivatives, Prentice Hall, 2005.
● Lamberton, D., and Lapeyre, B., Introduction to Stochastic Calculus Applied to Finance. Second Edition,
Chapman & Hall CRC, 2008.
● Pires, C.P., Mercados e Investimentos Financeiros, Escolar Editora, 3ª edição, 2011.

Teaching method

The content of the course is taught in theoretical-practical classes, during which interaction with students is stimulated. Problem sets with practical exercises to support understanding of the material covered in the theoretical classes are solved, to illustrate the theory.

Evaluation method

Available soon

Subject matter

1. Portfolio management
1.1. Optimal portfolio choice
1.2. Multi-factor models
1.3 Capital Asset Pricing Model --- CAPM
1.4. Arbitrage Models -- APT
1.5. Applications
2. Discrete models for financial markets
2.1. Binomial Model
2.2. Complete Markets and Arbitrage
2.3. Derivatives
2.4. Hedging
2.5. Dividends
2.6. Stochastic models of bonds and i nterest rates
2.7. Applications