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:

• Expositional sessions: Consists on the presentation of the topics of the course using the lecture notes and some papers previously distributed to the students.
• 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. The focus will be on the valuation of futures contracts, forwards and options and their hedging strategies. Another relevant objective is the numerical implementation of the models in Matlab or Python.

1. Financial derivatives: Futures, forwards, swaps and options; Market participants.

2. Futures and forwards: Pricing; Hedging strategies.

3. Options markets: Terminology; Basic positions and payoffs; Intrinsic value and time value; No-arbitrage restrictions; Put-call parity.

4. Hedging and speculation strategies: Hedging strategies; Speculation strategies on prices; Speculation strategies on volatility.

5. Binomial model: Single-period; Replication portfolio; Multi-period; American-style options; Dividends.

6. Black-Scholes-Merton model: Brownian motion, Itô’s lemma, GBM and fundamental PDE; Black-Scholes-Merton formula; Discrete dividends and dividend yield; Options on indices, currencies and futures.

7. Greeks: Delta hedging; Gamma hedging; Vega hedging; Dynamic portfolio insurance.

8. Volatility and correlation: Volatility smile; Estimation of volatility and correlation; Alternatives to the BSM model.

9. Structured products and exotic options: Components and static hedging; Binary options; Pay-later options; Forward start options; Exchange options; Compound options; As you like it options; Quanto options; Basket options; Barrier options; Lookback options; Asian options; Monte Carlo simulation.

Knowledge assessment will take place according to the following methods:

i. Evaluation through final examination

The final exam will consist of an individual written test, and students who obtain a rating equal to or greater than ten values will be approved.

 ii. Evaluation distributed throughout the semester

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

• Individual written test (60%);
• Group work with discussion (40%).

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.

NAO