Interest Rate Models

About this course: 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.

Who is this class for: This course is primarily aimed at advanced graduates interested in quantitative finance, along with finance professionals with an interest in interest rate models. Prerequisites for this course: elementary probability theory and real calculus. To solve the quizzes, students also need a matrix-oriented scientific computing package such as Matlab or R.

Created by:  École Polytechnique Fédérale de Lausanne

• Taught by:  Damir Filipović, EPFL

  The Swissquote Chair in Quantitative Finance and Swiss Finance Institute Professor

Level Advanced Commitment 5 weeks of study, 6 hours per week Language English How To Pass Pass all graded assignments to complete the course. User Ratings 4.5 stars Average User Rating 4.5See what learners said Coursework

Each course is like an interactive textbook, featuring pre-recorded videos, quizzes and projects.

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École Polytechnique Fédérale de Lausanne

Syllabus


WEEK 1


Introduction



1 video, 4 readings expand

1. Video: Introduction
2. Reading: Evaluation
3. Reading: Certificate
4. Reading: Course discussions
5. Reading: Where to get help

WEEK 2


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.


5 videos, 2 readings, 5 practice quizzes expand

1. Video: Interest Rates and Discount Bonds
2. Reading: Compounded Interest Rates
3. Practice Quiz: Interest Rates and Discount Bonds
4. Video: Forward and Futures Rates
5. Reading: Continuously Compounded Forward Rate (Forward Yield)
6. Practice Quiz: Forward and Futures Rates
7. Video: Coupon Bonds and Interest Rate Swaps
8. Practice Quiz: Coupon Bonds and Interest Rate Swaps
9. Video: Duration and Convexity
10. Practice Quiz: Duration and Convexity
11. Video: Market Conventions
12. Practice Quiz: Market Conventions

Graded: Interest Rates and Related Contracts

WEEK 3


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.


4 videos, 4 practice quizzes expand

1. Video: Bootstrapping Example
2. Practice Quiz: Bootstrapping Example
3. Video: Exact Methods
4. Practice Quiz: Exact Methods
5. Video: Smoothing Methods
6. Practice Quiz: Smoothing Methods
7. Video: Principal Component Analysis
8. Practice Quiz: Principal Component Analysis

Graded: Estimating the Term Structure

WEEK 4


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.


4 videos, 1 reading, 4 practice quizzes expand

1. Video: Stochastic Calculus
2. Reading: Definition of Brownian Motion without Filtration
3. Practice Quiz: Stochastic Calculus
4. Video: Short Rate Models
5. Practice Quiz: Short Rate Models
6. Video: Heath-Jarrow-Morton Framework
7. Practice Quiz: Heath-Jarrow-Morton Framework
8. Video: Forward Measures
9. Practice Quiz: Forward Measures

Graded: Stochastic Models

WEEK 5


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.


4 videos, 4 practice quizzes expand

1. Video: Interest Rate Futures and Convexity Adjustment
2. Practice Quiz: Interest Rate Futures and Convexity Adjustment
3. Video: Caps and Floors
4. Practice Quiz: Caps and Floors
5. Video: Swaptions
6. Practice Quiz: Swaptions
7. Video: Calibration Example
8. Practice Quiz: Calibration Example

Graded: Interest Rate Derivatives

WEEK 6


Final Quiz

Graded: Final quiz