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.

NAO

Basic:

• Dias, J.C. (2022). Lecture Notes, Iscte Business School.
• Hull, J.C. (2018). Options, Futures, and Other Derivatives, 10th edition, Pearson.

Complementary:

• Brandimarte, P. (2006). Numerical Methods in Finance and Economics: A Matlab-Based Introduction, 2nd edition, Wiley.
• Gatheral, J. (2006). The Volatility Surface: A Practitioner`s Guide, Wiley.
• Hilpisch, Y. (2015). Derivatives Analytics with Python: Data Analysis, Models, Simulation, Calibration and Hedging, Wiley.
• Kienitz, J. and Wetterau, D. (2012). Financial Modelling: Theory, Implementation and Practice (with Matlab Source), Wiley
• McDonald, R.L. (2013). Derivatives Markets, 3rd edition, Pearson.
• Rouah, F.D. (2013). The Heston Model and Its Extensions in Matlab and C#, Wiley.
• Rouah, F.D. (2015). The Heston Model and Its Extensions in VBA, Wiley.
• Rouah, F.D. and Vainberg, G. (2007). Option Pricing Models and Volatility Using Excel-VBA, Wiley.
• Zhang, P.G. (1998). Exotic Options: A Guide to Second Generation Options, 2nd edition, World Scientific Publishing.
• Several published articles.