## Interest Rate Models

Start Date: 07/05/2020

 Course Type: Common Course

Explore 1600+ online courses from top universities. Join Coursera today to learn data science, programming, business strategy, and more. 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.

#### Course Syllabus

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. #### Course Tag

Calibration Stochastic Calculus Yield Curve Interest Rate Derivative

#### Related Wiki Topic

Article Example
Stochastic investment model Interest rate models can be used to price fixed income products. They are usually divided into one-factor models and multi-factor assets.
Dynamic financial analysis The interest rate generator is the core fundamental of DFA. Many sophisticated interest rate models were created in the effort to best imitate the real world interest rate behavior. Although none of the existing models are perfect, they have their own advantages and disadvantages. The following is a simple interest rate model used in a publicly access DFA model.
Emanuel Derman He is a co-author of Black–Derman–Toy model, one of the first interest-rate models, and the Derman–Kani local volatility or implied tree model, a model consistent with the volatility smile.
Interest rate The nominal interest rate is the rate of interest with no adjustment for inflation.
Interest rate A so-called "negative interest rate policy" (NIRP) is a negative (below zero) central bank target interest rate.
Effective interest rate The effective interest rate, effective annual interest rate, annual equivalent rate (AER) or simply effective rate is the interest rate on a loan or financial product restated from the nominal interest rate as an interest rate with annual compound interest payable in arrears.
Interest rate The real interest rate is given by the Fisher equation:
Interest rate Annual interest rate is the rate over a period of one year. Other interest rates apply over different periods, such as a month or a day, but they are usually annualised.
Interest rate An interest rate, is the amount of interest due per period, as a proportion of the amount lent, deposited or borrowed (called the principal sum). The total interest on an amount lent or borrowed depends on the principal sum, the interest rate, the compounding frequency, and the length of time over which it is lent, deposited or borrowed.
Interest rate The "spread" of interest rates is the lending rate minus the deposit rate. This spread covers operating costs for banks providing loans and deposits. A "negative spread" is where a deposit rate is higher than the lending rate.
Interest rate future Short-term interest rate futures are extensively used in the hedging of interest rate swaps.
Floating interest rate Certain types of floating rate loans, particularly mortgages, may have other special features such as interest rate caps, or limits on the maximum interest rate or maximum change in the interest rate that is allowable.
Interest rate The elasticity of substitution (full name is the marginal rate of substitution of the relative allocation) affects the real interest rate. The larger the magnitude of the elasticity of substitution, the more the exchange, and the lower the real interest rate.
Interest rate According to the theory of rational expectations, borrowers and lenders form an expectation of inflation in the future. The acceptable nominal interest rate at which they are willing and able to borrow or lend includes the real interest rate they require to receive, or are willing and able to pay, plus the rate of inflation they expect.
Interest rate A so-called "zero interest rate policy" (ZIRP) is a very low—near-zero—central bank target interest rate. At this zero lower bound the central bank faces difficulties with conventional monetary policy, because it is generally believed that market interest rates cannot realistically be pushed down into negative territory.
Real interest rate The real interest rate is the rate of interest an investor, saver or lender receives (or expects to receive) after allowing for inflation. It can be described more formally by the Fisher equation, which states that the real interest rate is approximately the nominal interest rate minus the inflation rate.
Interest rate swap Hedging interest rate swaps can be complicated and relies on numerical processes of well designed risk models to suggest reliable benchmark trades that mitigate all market risks. The other, aforementioned risks must be hedged using other systematic processes.
Nominal interest rate The nominal interest rate (also known as an Annualised Percentage Rate or APR) is the periodic interest rate multiplied by the number of periods per year. For example, a nominal annual interest rate of 12% based on monthly compounding means a 1% interest rate per month (compounded). A nominal interest rate for compounding periods less than a year is always lower than the equivalent rate with annual compounding (this immediately follows from elementary algebraic manipulations of the formula for compound interest). Note that a nominal rate without the compounding frequency is not fully defined: for any interest rate, the effective interest rate cannot be specified without knowing the compounding frequency "and" the rate. Although some conventions are used where the compounding frequency is understood, consumers in particular may fail to understand the importance of knowing the effective rate.
Nominal interest rate Example 1: A nominal interest rate of 6%/a compounded monthly is equivalent to an effective interest rate of 6.17%.
Nominal interest rate In finance and economics, nominal interest rate or nominal rate of interest refers to two distinct things: