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.
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Interest Rate Models
École polytechnique fédérale de LausanneÀ propos de ce cours
Résultats de carrière des étudiants
50%
40%
Compétences que vous acquerrez
Résultats de carrière des étudiants
50%
40%
Programme du cours : ce que vous apprendrez dans ce cours
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.
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Meilleurs avis pour INTEREST RATE MODELS
Solid contents, also required solid graduate level mathematics. The instructor may consider providing more details in some of the derivations. It is a bit difficult to follow during some lectures.
This course is very good in regaining your knowledge in Interest Rate model. However, the exchange is that you have to spend time with it. But believe me it is worth your time spending
This course was very interesting and a bit hard for me, specially those topics involving measure theory. I'd like to thank to the course moderators and their helpfully advices.
Very engaging materials and it is a difficult course!! Background in linear algebra, stochastic calculus and computer programming is recommended.
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