Derivatives Markets

Even though there are no formal pre-requisites, basic knowledge of calculus and statistics are welcomed.

The teaching methodology will be based on the following format and teaching methods:

• ME1. Expositional sessions: Consists on the presentation of the topics of the course using the lecture notes and some papers previously distributed to the students.
• ME2. Practical sessions: All the expositional sessions will be complemented through an intensive use of practical examples in Excel and/or Matlab and/or Python to discuss and solve some of the methodological and computational issues of the covered subjects.

This curricular unit aims to provide students with an in-depth knowledge about theoretical and practical aspects of financial derivatives.

Upon completion of the course unit, the student will be able to:

• LO1: Value futures, forwards, and options contracts and construct derivatives hedging strategies.
• LO2: Implement derivatives valuation and hedging models in Matlab or Python.

Associated competencies:

• CD1: Critical thinking: ability to analytically evaluate and hedge financial derivatives.
• CD2: Programming and communication: demonstrate programming skills in Matlab or Python for valuing derivative instruments, as well as oral presentation skills and the ability to technically defend the proposed solutions.

P1. Financial derivatives

1.1. Futures, forwards, swaps and options

1.2. Market participants

P2. Futures and forwards

2.1. Pricing

2.2. Hedging strategies

P3. Options markets

3.1. Terminology

3.2. Basic positions and payoffs

3.3. Intrinsic value and time value

3.4. No-arbitrage restrictions

3.5. Put-call parity

P4. Hedging and speculation strategies

4.1. Hedging strategies

4.2. Speculation strategies on prices

4.3. Speculation strategies on volatility

P5. Binomial model

5.1. Single-period

5.2. Replication portfolio

5.3. Multi-period

5.4. American-style options

5.5. Dividends

P6. Black-Scholes-Merton model

6.1. Brownian motion, Itô’s lemma, GBM and fundamental PDE

6.2. Black-Scholes-Merton formula

6.3. Discrete dividends and dividend yield

6.4. Options on indices, currencies and futures

P7. Greeks

7.1. Delta hedging

7.2. Gamma hedging

7.3. Vega hedging

7.4. Dynamic portfolio insurance

P8. Volatility and correlation

8.1. Volatility smile

8.2. Estimation of volatility and correlation

8.3. Alternatives to the BSM model

P9. Structured products and exotic options

9.1. Components and static hedging

9.2. Binary options

9.3. Forward start options

9.4. Exchange options

9.5. Compound options

9.6. As you like it options

9.7. Quanto options

9.8. Basket options

9.9. Barrier options

9.10. Lookback options

9.11. Asian options

9.12. Monte Carlo simulation

9.13. Volatility derivatives

Knowledge assessment will take place according to the following methods:

A) Continuous/periodic evaluation

The evaluation of knowledge distributed throughout the semester will take place as follows:

• MA1. Individual written test (60%): without consultation and with minimum grade of 8 points.
• MA2. Group work with oral discussion and defense (40%): minimum grade of 10 points.

The individual written test will consist of the normal season exam, and the respective classification cannot be less than eight points. Each working group must have 3 students, though may have a different composition subject to the approval of the responsible for the curricular unit. This classification cannot be less than ten points.

Students who have obtained a final average resulting from the classifications obtained in the individual written test and in the group work of at least ten points will be considered approved, provided that the minimum score of each of the evaluation elements has been reached. If any of the minimum grades have not been reached, the student fails being awarded the grade of the rating element with the lowest score.

The work should focus on one of the following topics:

• Valuation and hedging of a futures contract;
• Valuation and hedging of a standard options contract;
• Valuation and hedging of a structured product;
• Valuation and hedging of an exotic option.

Final grade formula:

CF = 0.60 x MA1 + 0.40 x MA2

B) Evaluation through exam (1st/2nd/3rd sittings)

• MA3. Individual written test (100%): without consultation and with minimum grade of 9.5 points.

Exam formula:

CF = 1.00 x MA3

In both evaluation possibilities (A and B) and where there are reasonable grounds to suspect fraud detected during the exam-marking process, the student will be required to take an oral examination to verify the knowledge and skills demonstrated. This assessment will be conducted by a panel comprising the course unit lecturer and two other lecturers from the same subject area. If the student is unable to demonstrate the knowledge and skills shown in the written examination, the examination will be annulled.

NAO