# Financial Mathematics

## Objectives

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

##### Code

12236

##### Credits

6.0

##### Responsible teacher

Pedro José dos Santos Palhinhas Mota

##### Hours

Weekly - 4

Total - 56

##### Teaching language

Português

### Prerequisites

Basic knowledge of Mathematical Analysis and Probability and Statistics.

### Bibliography

● 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

**1 - Frequency**

Attendance is given to students who attend at least two thirds of the classes.

**2 - Continuous Assessment**

The continuous assessment of the curricular unit is achieved with two tests (T1 and T2), to be carried out during the academic period.

Each of the tests will be assigned a classification (CT1 and CT2) between 0 and 20 values. A student who meets the frequency criterion explained above will have a final continuous assessment classification equal to (CT1+CT2)/2, rounded to the nearest integer.

The student will obtain approval in the curricular unit if this classification is greater than or equal to 10 points.

**3 – Assessment with Final Exam**

Students who fail the continuous assessment, who have obtained frequency in the curricular unit or who have been exempt from it, may take a supplementary test, hereinafter referred to as Exam (E).

The Exam consists of a written test, which evaluates all the content taught in the curricular unit. The exam is divided into two parts, EP1 and EP2, whose material assessed corresponds, respectively, to that assessed in continuous assessment at T1 and T2.

The Exam will be assigned a classification (CE) between 0 and 20 values, with the student''s final classification being equal to the classification obtained, rounded to the nearest integer.

The student will obtain approval in the curricular unit if this classification is greater than or equal to 10 points. Otherwise, the student will have failed the course.

**4 - Grade Defense**

All students with a final grade above 18 may, if they wish, take a grade defense test. Failure to take this test implies a final grade of 18 points for the curricular unit.

**5 - Ranking Improvement**

Students approved in the curricular unit may request, upon compliance with all provisions imposed by FCT NOVA, Classification Improvement.

## 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 interest rates

2.7. Applications

## Programs

Programs where the course is taught: