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École Polytechnique Fédérale de Lausanne

Interest Rate Models

École Polytechnique Fédérale de Lausanne via Coursera

Overview

This course gives you an easy introduction to interest rates and related contracts. These include the LIBOR, bonds, forward rate agreements, swaps, interest rate futures, caps, floors, and swaptions. We will learn how to apply the basic tools duration and convexity for managing the interest rate risk of a bond portfolio. We will gain practice in estimating the term structure from market data. We will learn the basic facts from stochastic calculus that will enable you to engineer a large variety of stochastic interest rate models. In this context, we will also review the arbitrage pricing theorem that provides the foundation for pricing financial derivatives. We will also cover the industry standard Black and Bachelier formulas for pricing caps, floors, and swaptions.

At the end of this course you will know how to calibrate an interest rate model to market data and how to price interest rate derivatives.

Syllabus

  • Introduction
  • Interest Rates and Related Contracts
    • We learn various notions of interest rates and some related contracts. Interest is the rent paid on a loan. A bond is the securitized form of a loan. There exist coupon paying bonds and zero-coupon bonds. The latter are also called discount bonds. Interest rates and bond prices depend on their maturity. The term structure is the function that maps the maturity to the corresponding interest rate or bond price. An important reference rate for many interest rate contracts is the LIBOR (London Interbank Offered Rate). Loans can be borrowed over future time intervals at rates that are agreed upon today. These rates are called forward or futures rates, depending on the type of the agreement. In an interest rate swap, counterparties exchange a stream of fixed-rate payments for a stream of floating-rate payments typically indexed to LIBOR. Duration and convexity are the basic tools for managing the interest rate risk inherent in a bond portfolio. We also review some of the most common market conventions that come along with interest rate market data.
  • Estimating the Term Structure
    • We learn how to estimate the term structure from market data. There are two types of methods. Exact methods produce term structures that exactly match the market data. This comes at the cost of somewhat irregular shapes. Smooth methods penalize irregular shapes and trade off exactness of fit versus regularity of the term structure. We will also see what principal component analysis tells us about the basic shapes of the term structure.
  • Stochastic Models
    • Models for the evolution of the term structure of interest rates build on stochastic calculus. We start with a crash course in stochastic calculus, which introduces Brownian motion, stochastic integration, and stochastic processes without going into mathematical details. This provides the necessary tools to engineer a large variety of stochastic interest rate models. We then study some of the most prevalent so-called short rate models and Heath-Jarrow-Morton models. We also review the arbitrage pricing theorem from finance that provides the foundation for pricing financial derivatives. As an application we price options on bonds.
  • Interest Rate Derivatives
    • We apply what we learnt to price interest rate derivatives. Specifically, we focus on the standard derivatives: interest rate futures, caps and floors, and swaptions. We derive the industry standard Black and Bachelier formulas for cap, floor, and swaption prices. In a case study we learn how to calibrate a stochastic interest rate model to market data.
  • Final Quiz

Taught by

Damir Filipović

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Reviews

3.2 rating, based on 6 reviews

Start your review of Interest Rate Models

  • Brian J Crone is taking this course right now.

    the description of this class is that its an easy introduction to interest rate models. this is complete nonsense they should state it might be easy if you have a ph.d in stochastic calculus. the lecture slides are ambiguous and totally confusing....
  • Anonymous

    Anonymous is taking this course right now.

    Video lectures are almost useless. The slides are very compact and the "lecturer" just reads them! no insight!
    The quizzes though practical, are disproportionally harder than the material presented on the lectures, there isnt even a step by step difficulty rising!

    I glanced over forward measures material...and...good luck, unless you already know the stuff and it acts as a reminder there is 0 chance to learn it from here.

    1star rating due to inaccurate course description.
  • Profile image for Felix Camacho
    Felix Camacho

    Felix Camacho completed this course, spending 20 hours a week on it and found the course difficulty to be very hard.

    An excellent course, the material presented is quite advanced for a MOOC. Short, austere videos and slides that are very rich in content despite their rather compact presentation. Do not be fooled by the description - this is far from an "easy" introduction...
  • Anonymous

    Anonymous completed this course.

    Difficult but very interesting course. Give a clear introduction to quantitative finance but on the other hand, it does not give enough references, link to article to go deeper into subject
  • Profile image for DietCoke
    DietCoke
    27

    DietCoke is taking this course right now, spending 10 hours a week on it and found the course difficulty to be hard.

    This is an advanced course for people in quantitative finance field ONLY. Those who lack related background may find it very difficult but it is a good course for people in quant field.
  • Richard Van Egas is taking this course right now, spending 20 hours a week on it and found the course difficulty to be very hard.

    Well, where to start with?? The class contents and lecture slides will not help you to answer the practice quizzes. The practice quizzes do not have a guide telling you what should you do? From the above, the actual graded quiz is a non sense . None...

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