Applied Derivatives


Structured securities allow retail investors to take a (covered) position on the performance of (almost) any underlying asset, and are becoming increasing popular in Europe and in the US. For instance, in 2010 the US structured products market sold more than $53bn of notional value. However, the non- traditional (and complex) payoffs offered by such over-the-counter (OTC) structured products are often based on portfolios of non-standard (i.e. exotic) financial options.

This course is mainly devoted to the pricing of exotic options and structured products, under the usual Black-Scholes-Merton assumptions. After describing each structured product, the valuation of the embedded exotic options will be discussed, and the issuer’s hedging strategy will be defined. Special attention is devoted to the analysis of barrier (path-dependent) options.

Additionally, the last four lectures will cover the hedging and pricing of the most liquid OTC interest rate products: Caps, floors, collars and swaptions.

According to the September 2014 BIS Quarterly Review (Bank for International Settlements), the total notional principal amount of OTC interest rate options such as caps/floors and swaptions outstanding at the end of December 2013 was about $49.3 trillion. The valuation of these contracts will be based on the LIBOR market model, and caps, floors and collars will be synthetized through the Eurodollar futures option market.

General characterization





Responsible teacher

João Pedro Vidal Nunes


Weekly - Available soon

Total - Available soon

Teaching language





Brigo, D., and F. Mercurio, Interest Rate Models - Theory and Practice: With Smile, Inflation and Credit, Springer Finance, 2006, 2nd edition. (optional).

Briys, E., M. Bellalah, H. M. Mai and F. De Varenne, Options, Futures, and Exotic Derivatives, Wiley, 1998. (optional).

Hull, John C., Options, Futures, and Other Derivative Securities, Prentice Hall, 9th edition, 2014. (mandatory).

Zhang, P., Exotic Options: A Guide to Second Generation Options, World Scientific, 1998, 2nd edition. (optional).

Other resources: Class notes, class handouts, research papers and exercises.

Teaching method

The course will be based on 12 lectures, 2 per week. During classes, real-life examples based on traded products and on financial data collected from the Bloomberg system will be presented. Students are required to solve homework assignments every 2 weeks. Students are also required to solve one Case Study. There is a comprehensive final exam where the whole syllabus will be tested.

Evaluation method

The final exam is mandatory and must cover the entire span of the course. Its weight in the final grade can be between 30 to 70%. The remainder of the evaluation can consist of class participation, midterm exams, in class tests, etc. Overall, written in class assessment (final exam, midterm) must have a weight of at least 50%.

The final grade of each student attending this course will correspond to the weighted average between the following three components:

  • One individual, mandatory, and open book written exam: (60%)

  • Individual homework assignments: (20%)

  • One group assessment case comprising the evaluation of a structured product: (20%)

Class participation is welcome and contributes to the rounding up of the final grade. Note that, in accordance with the school’s norms, there is no procedure for grade improvement after passing a course (no re-sit or second course enrolment).

Subject matter

The course comprises 12 sessions of 1h20m each. We will cover the following topics:

  • 1. Structured products:

    a. Components;

    b. Static hedging;

    c. First example: Vertical bullish spread.

  • 2. Binary options:

    a. Cash-or-nothing options;

    b. Range accrual notes.

  • 3. Forward-start options:

    a. On the price;

    b. On the rate of return.

  • 4. Barrier options:

    a. Payoffs;

    b. Restricted densities;

    c. Knock-in options;

    d. Knock-out options;

    e. Static hedging;

    f. Rebates;

    g. Monte Carlo simulation.

  • 5. Options on Eurodollar futures:

    a. Synthetic caps, floors and collars;

    b. Futures-style margining.

  • 6. LIBOR market model:

    a. General setup;

    b. Black model;

    c. Caps, floors and collars;

    d. Swaptions.


Programs where the course is taught: