Fixed Income


Fixed income securities include bonds that promise a fixed income stream and also other securities with contingent payments whose valuation depends on interest rates. Fixed income is one of the largest financial markets. For example, at the end of 2011 the U.S. government debt stood at 9.9 trillion USD (expected to keep rising); also, the notional value of the interest rate swap market was 402 trillion USD. From the corporate side, effective interest rate risk management is essential. Another example like, more than 90% of the world s largest 500 companies, use fixed income derivatives to manage their interest rate risk exposure.

This course covers the main models and techniques used to analyze fixed income instruments and their derivatives. The course aims to provide students with the concepts and tools that money managers and risk managers use every day to decide on how to allocate investments or to manage the interest rate risk exposure of mutual funds, hedge funds, insurance companies, investment banks, and other large nonfinancial firms.

General characterization





Responsible teacher

João Pedro Pereira


Weekly - Available soon

Total - Available soon

Teaching language




A set of handouts will be distributed in class. They are based on the following books:

1. Veronesi. Fixed income securities: valuation, risk, and risk management. John Wiley & Sons, 2011.

a. has solutions to exercises and other resources.

2. Hull. Options, futures, and other derivatives. Pearson, 8th ed, 2012. (or newer edition)

3. Tuckman and Serrat. Fixed Income Securities. John Wiley and Sons, 2011.

Teaching method

1.    Reviewing the content of the lectures and related bibliography.
2.    Solving homework problems

Evaluation method

The final grade is computed from the following:
•    Final exam
o    The exam is closed-book and closed-notes. However, you may use a two-sided A4 formula sheet and a pocket calculator.
o    The minimum grade in the final exam to pass the course is 6.
•    Cases and Problem sets
o    There will be regular homework assignments. The assignments will consist of small end-of-chapter problems, as well as larger projects that will require some computer work.
o    The assignments should be done in groups of one, two (recommended), or three people.
o    Please submit your answers through Moodle.
o    Some questions in the problem sets may not be graded.
•    Quizzes
o    Small problems to be solved individually in class
o    The problems will be similar to the ones done in class or in the homework problems.
o    The quizzes are open-book and open-notes. Laptops must be off, though.
o    Please bring a pocket calculator to every class. Cellphones are not allowed.
o    The quizzes are unannounced.
o    You must take the quiz in the section in which you are enrolled. Quizzes submitted in the “wrong section” will not be graded.
o    If you are not in class on the day of the quiz, you may not take it at a later date. The “free option” below is intended to compensate for quizzes that you miss for whatever reason, and other idiosyncratic events.

Weights: I will compute the following two options and assign you the highest result:

         Option A        Option B   
Final exam    50%    70%
Cases and Problem Sets    30%    30%
Quizzes    20%    0%
Class participation counts towards rounding the final grade. Good class participation consists of asking informed questions or making informed comments that improve the overall learning of the class, as well as answering the questions asked in class.

Any instance of cheating will be penalized with a failing grade in the whole course.
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 has 12 sessions of 1h20m. We will cover the following topics:

  • 1. Basics of fixed income:

    a. Markets and securities;

    b. Price quotes;

    c. Discount factors and interest rates;

    d. Fixed-coupon bonds;

    e. Floating-rate bonds;

    Readings: Veronesi, ch 1, 2.

  • 2. Yield curve fitting:

    a. Bootstrap;

    b. Nelson and Siegel model;

    c. Svensson model;

    Readings: Veronesi, ch 2.4.2, 2.9.3

  • 3. Bond portfolio management:

    a. Duration;

    b. Immunization;

    c. Asset-Liability management;

    d. Convexity;

    Readings: Veronesi, ch 3, 4.1

  • 4. Interest rate derivatives:

    a. Forward Rate Agreements;

    i. Hedging with FRA;

    ii. Pricing FRA;

    b. Interest rate swaps;

    i. Hedging with IRS;

    ii. Pricing IRS;

    iii. The swap curve;

    iv. Asset-Liability management with IRS;

    c. Forward contracts;

    i. Hedging with Forward contracts;

    ii. Pricing Forward contracts;

    d. Interest rate futures;

    i. Eurodollar futures;

    1. Hedging with Eurodollar futures;

    2. Extending the LIBOR zero curve;

    ii. Treasury bond futures;

    1. Cheapest to deliver;

    2. Hedging with T-bond futures;

    e. Interest rate options;

    i. Bond options;

    ii. Caps and floors.

    Readings: Veronesi, ch 5, 6; Hull, ch 4, 6, 7, 28

  • 5. Term structure dynamics: Vasicek model.

    a. Bond prices;

    b. Estimating the parameters;

    c. Prices of options on zero-coupon bonds.

    Readings: Veronesi, ch 15