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.
Introduction
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From the course by École Polytechnique Fédérale de Lausanne
Interest Rate Models
77 ratings
Meet the Instructors
Damir FilipovićEPFL
The Swissquote Chair in Quantitative Finance and Swiss Finance Institute Professor
Welcome to the M.O.O.C on interest rate models.
I'm Damir Filipovic, and I will be your professor for this course.
A component that is common to various financial products
and transactions, is the interest rate.
Interest is the rent paid for a loan of money
over a period of time.
Interest exists because an amount of money has a different value
at different times.
Interest accounts for these value changes.
Interest is the time value of money.
Interest rates themselves change over time
because the economy changes.
Future interest rates are as uncertain
as the future state of the economy is.
Stochastic models for the evolution of interest rates
are an important ingredient for financial risk management
and the pricing of interest rate products.
The volume of such products indeed is huge.
The outstanding notional amount is in the order of
hundreds of trillions of U.S dollars currently.
This course gives you an introduction to stochastic interest rate models.
It consists of the 4 parts as shown here.
And I will now briefly comment on each part separately.
In the first part, I introduce the notion of interest rates
and some related basic contracts.
A bond is the securitized, that is, tradable form of a loan.
There exist coupon paying bonds and zero coupon bonds.
The latter, are also called discount bonds.
The price of a discount bond is simply
the present value of a cash flow, of one unit of currency
at some future maturity date.
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 L.I.B.O.R.
The London Inter-Bank Offered Rate.
It is daily fixed for various currencies and maturities.
Loans can also 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, counter parties exchange
a stream of fixed rate payments
for a stream of floating rate payments.
Typically indexed to L.I.B.O.R of a particular maturity.
When it comes to managing the interest rate risk
of a bond portfolio, Duration and Convexity are the basic tools.
We will also review some of the most common market conventions
that come along with interest rate market data.
In the second part, we will learn how to estimate
the term structure for market data.
There are 2 types of methods.
Exact methods produce term structures that exactly match the market data.
This comes at a cost of somewhat irregular shapes of the term structure.
Smooth methods penalize irregualar 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.
Models for the evolution of the term structure of interest rates
build on stochastic calculus.
In the third part, I will give a crash course in stochastic calculus.
I will introduce Brownian motion, stochastic integration and processes,
but without going into mathematical details.
The good news is that this will give you the necessary tools
to engineer a large variety of stochastic interest rate models.
We will then study some of the most prevalent
so called, Short rate models, and Heath-Jarrow-Morton models.
I will also review the arbitrage pricing theorem from finance.
That provides the foundation for pricing financial derivatives.
Eventually, we will see how we can use these models
to price options on bonds.
In the fourth part, we will then apply what we learned
to price interest rate derivatives.
Specifically, we will focus on the standard derivatives,
interest rate futures, caps and floors, and swaptions.
We will see and understand
the industry standard Black and Bachelier formulas
for cap, floor, and swaption prices.
And eventually in a case study
we will see how to calibrate a stochastic interest rate model
to market data.
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