There are 2 broad approaches to model the term structure of interest rates:

1.

2.

There are 2 broad approaches to model the term structure of interest rates:

1. Equilibrium

2. Arbitrage-free

___ models for modeling the term structure for interest rates assume a process for short-term interest rates and then use that process to look at the expected path of future interest rates.

**Equilibrium** models for modeling the term structure for interest rates assume a process for short-term interest rates and then use that process to look at the expected path of future interest rates.

___-___models for modeling future interest rates project future interest rates in such a way that they are consistent with the observed term structure.

**Arbitrage-free** models for modeling future interest rates project future interest rates in such a way that they are consistent with the observed term structure.

___ term structure model is a single-factor model that assumes that the short-term interest rate drifts toward a specific long-term mean.

**Vasicek's **term structure model is a single-factor model that assumes that the short-term interest rate drifts toward a specific long-term mean.

Vasicek's Model

Yield to Maturity in Vasicek

CIR Model (Equation)

A criticism of the Vasicek model is that it assumes the ___ of changes in the interest rates is constant as the ___ of interest rate changes.

A criticism of the Vasicek model is that it assumes the **volatility **of changes in the interest rates is constant as the **level **of interest rate changes.

Ho and Lee Model

Conditional Prepayment Rate (CPR)

Absolute Prepayment Speed (ABS)

Single Monthly Mortality (SMM)

The ___, ___and ___ model modified the Vasicek model so that the variance of the short-term rate is proportional to the rate itself.

The **Cox**, **Ingersoll **and **Ross **(CIR) model modified the Vasicek model so that the variance of the short-term rate is proportional to the rate itself.

___-___models of the term structure generate bonds that do not allow for arbitrage opportunities.

**Arbitrage**-**free **models of the term structure generate bonds that do not allow for arbitrage opportunities.

The ___ and ___model assumes that the short-term interest rate follows a normally distributed process, with a drift parameter selected so that the modeled interest rates fit the observed structure of interest rates.

The **Ho **and **Lee **model assumes that the short-term interest rate follows a normally distributed process, with a drift parameter selected so that the modeled interest rates fit the observed structure of interest rates.

The key disadvantage of the Ho and Lee model are that it assumes a very simple ___ process for bond prices and it can produce ___interest rates.

The key disadvantage of the Ho and Lee model are that it assumes a very simple **binomial **process for bond prices and it can produce **negative **interest rates.

An ___ ___ ___is an interest rate derivative in which one party pays the other party when a specified reference rate exceeds a specific cap rate.

An **interest rate cap **is an interest rate derivative in which one party pays the other party when a specified reference rate exceeds a specific cap rate.

A ___ is an interest rate cap that is guaranteed for one specific date.

A **caplet **is an interest rate cap that is guaranteed for one specific date.

A ___ is a series of caplets and its price equals the sum of the caplet prices.

A **cap **is a series of caplets and its price equals the sum of the caplet prices.

An ___ ___ ___ is an interest rate derivative in which one party pays the other when a specified reference rate is below a floor rate.

An **interest rate floor **is an interest rate derivative in which one party pays the other when a specified reference rate is below a floor rate.

A ___ is an interest rate floor guaranteed for one specific date.

A **floorlet **is an interest rate floor guaranteed for one specific date.

A ___ is a series of floorlets and its price equals the sum of the floorlet prices.

A **floor **is a series of floorlets and its price equals the sum of the floorlet prices.

Issuers of floating rate debt can buy interest rate ___ to hedge their exposure.

Issuers of floating rate debt can buy interest rate **caps **to hedge their exposure.

Lenders of floating-rate debt can buy interest rate ___ to hedge their exposure.

Lenders of floating-rate debt can buy interest rate **floors **to hedge their exposure.

Since caps and floors are not typically exchange-traded instruments, buyers of these derivatives are exposed to ___ risk.

Since caps and floors are not typically exchange-traded instruments, buyers of these derivatives are exposed to **counterparty **risk.

___ ___are bonds that can be redeemed by the bond issuer before maturity by making a set payment to the investor in a designated period.

**Callable bonds **are bonds that can be redeemed by the bond issuer before maturity by making a set payment to the investor in a designated period.

Bond pricing models should account not only for interest rate risk but also for ___ risk.

Bond pricing models should account not only for interest rate risk but also for **credit **risk.

Ignoring counterparty risk, payers in vanilla swaps benefit from ___ rates and suffer when rates ___.

Ignoring counterparty risk, payers in vanilla swaps benefit from **increased **rates and suffer when rates **decline**.

Ignoring counterparty risk, receivers in vanilla swaps benefit from ___ rates and suffer when rates ___.

Ignoring counterparty risk, receivers in vanilla swaps benefit from **declining **rates and suffer when rates **increase**.

Pension funds can use ___ ___ ___ or ___-___ ___ to reduce their interest rate risk.

Pension funds can use **interest rates swaps **or **long**-**term bonds **to reduce their interest rate risk.