Interest Rate Models

École Polytechnique Fédérale de Lausanne via Coursera

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Provider

Coursera
Pricing

Free Online Course (Audit)
Languages

English
Certificate

Paid Certificate Available
Duration & workload

1 day 5 hours 57 minutes
Sessions

On-Demand
Level

Advanced
Subtitles

Arabic, French, Portuguese, Italian, German, Russian, English, Spanish, Kazakh, Hindi, Swedish, Korean, Greek, Chinese, Thai, Ukrainian, Japanese, Indonesian, Polish, Dutch, Turkish, Hungarian, Bengali, Pashto, Urdu, Azerbaijani, Farsi

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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

Reviews

3.4 rating, based on 7 Class Central reviews

4.5 rating at Coursera based on 187 ratings

Start your review of Interest Rate Models

Brian J Crone

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.…

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. there are no worked examples explaining the concepts clearly. the assignments particularly the ones requireing calibratiion of various term structure models are utterly ridiculous the main problem being dealing with large matrices and getting the daycounts right. While this may be what a team might be faced with in a large Ibank for the purpose of a student learning this for the first time its completely ridiculous as it renders the assignments virtually impossible for someone just trying to learn. The quizes and assignments would make it look like they could be done in a few hours. The reality is a single problem could take a week. The notation used in this class is a complete nightmare. The class does not really provide many examples of how to calibrate interest rate models. This class could be made better if it provided proper fully worked examples of models like black derman toy, hull white, hjm and even current models. While the class technically lasts about six weeks it might take over six months to get through it. I dont know how many people actually make it through to the end of this class but i would imagine it is a small percentage. The main book for the class very quickly goes off he deep end and becomes an incomprehensible nightmare with no worked examples. I would like to complete this class but I had to take a break due to the fact it takes over. The videos for the class are virtually useless and the fact that there are zero fully worked examples and I mean zero makes it virtually impossible. Even simple models are rendered virtually impossible due to the awful notation used.
Anonymous

A similar opinion to Brian J Crone. The slides while concise, lack explanatory examples, and the lecturer merely reads them. The descriptions for numerical answer questions lack clear indications.
Anonymous

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.
Anonymous

A class of great quality provided by Damir Filipović and enable to deep dive into interest rates related contracts and models that enable to value them.
The rythme of the speech given by Damir is really good and the slides are of great support.

Thanks!
Anonymous

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
DietCoke

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.
Felix Camacho

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" intr…

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 to the subject matter. Linear algebra, stochastic calculus and the basic results of mathematical finance in continous time are necessary prerequisites in terms of theory. Basic programming skills with any language such as Python or R are also indispensable for the exercises, which require a lot of time to be completed succesfully.

Time commitment to the course grows greatly starting with Week 3, and by the final quiz it can feel quite overwhelming and frustrating due to the amount of material covered in each week and the high difficulty of some of the exercises. Still, it is quite doable (I finished a few days earlier than the schedule), but the effort required is not trivial. A good companion to the course is the book written by the Instructor, "Term-Structure Models", published by Springer.