Lecture

Interest Rate Models: Introduction

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Description

This lecture introduces the concept of interest rates, their importance in financial products, and the need for stochastic models to manage risk and price interest rate products. It covers basic contracts, term structures, interest rate swaps, market data estimation, stochastic calculus, short-rate models, and pricing of interest rate derivatives.

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Related concepts (31)

Interest rate derivative

In finance, an interest rate derivative (IRD) is a derivative whose payments are determined through calculation techniques where the underlying benchmark product is an interest rate, or set of different interest rates. There are a multitude of different interest rate indices that can be used in this definition. IRDs are popular with all financial market participants given the need for almost any area of finance to either hedge or speculate on the movement of interest rates.

Interest rate swap

In finance, an interest rate swap (IRS) is an interest rate derivative (IRD). It involves exchange of interest rates between two parties. In particular it is a "linear" IRD and one of the most liquid, benchmark products. It has associations with forward rate agreements (FRAs), and with zero coupon swaps (ZCSs). In its December 2014 statistics release, the Bank for International Settlements reported that interest rate swaps were the largest component of the global OTC derivative market, representing 60%, with the notional amount outstanding in OTC interest rate swaps of

381 trillion, and the gross market value of

14 trillion.

Stochastic differential equation

A stochastic differential equation (SDE) is a differential equation in which one or more of the terms is a stochastic process, resulting in a solution which is also a stochastic process. SDEs have many applications throughout pure mathematics and are used to model various behaviours of stochastic models such as stock prices, random growth models or physical systems that are subjected to thermal fluctuations. SDEs have a random differential that is in the most basic case random white noise calculated as the derivative of a Brownian motion or more generally a semimartingale.

Interest

In finance and economics, interest is payment from a borrower or deposit-taking financial institution to a lender or depositor of an amount above repayment of the principal sum (that is, the amount borrowed), at a particular rate. It is distinct from a fee which the borrower may pay to the lender or some third party. It is also distinct from dividend which is paid by a company to its shareholders (owners) from its profit or reserve, but not at a particular rate decided beforehand, rather on a pro rata basis as a share in the reward gained by risk taking entrepreneurs when the revenue earned exceeds the total costs.

Stochastic process

In probability theory and related fields, a stochastic (stəˈkæstɪk) or random process is a mathematical object usually defined as a sequence of random variables, where the index of the sequence has the interpretation of time. Stochastic processes are widely used as mathematical models of systems and phenomena that appear to vary in a random manner. Examples include the growth of a bacterial population, an electrical current fluctuating due to thermal noise, or the movement of a gas molecule.

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