Question 1

In the Vasicek one factor model, the short rate determines the model. In the Vasicek two factor model, what rates drive the model?

Accepted Answer

In the two factor model it is the short rate and the long rate that determine the rest of the rate dynamics in the term structure.

Question 2

Under the Vasicek model, what degree of correlation do diﬀerent interest rates have?

Accepted Answer

Rates on the term structure are perfectly correlated in the Vasicek model.

Question 3

When are multifactor models used?

Accepted Answer

When we want to allow independent variation in the level, slope and cur- vature components of the yield curve.

Question 4

How is the multivariate Ito's lemma deﬁned?

Accepted Answer

The answer of How is the multivariate Ito's lemma deﬁned?...

Question 5

What are multifactor models?

Accepted Answer

Multifactor models are models

Question 6

What is the diﬀerence between using a model for ﬁnding arbitrage oppor- tunities and using a model for pricing derivatives and other securities?

Accepted Answer

In the ﬁrst case we assume that our mode

Question 7

Is the 2-factor Vasicek model an aﬁne model?

Accepted Answer

Yes, it is an aﬁne m

Question 8

Can a solution always be found in order to price a security as proposed by the Feynman-Kac formula?

Accepted Answer

It is not always posible to ﬁn

Question 9

Does the 2-factor Vasicek model ﬁt the yield curve?

Accepted Answer

No, one of its main

Question 10

What peculiarity of a yield curve steepner makes the use of 2-factor models attractive?

Accepted Answer

A yield curve steepner depends on the re

Question 11

What modi?cations should be included to Ito's lemma when we allow correlation between the two factors?

Accepted Answer

The following term

Question 12

Show that, given:

Accepted Answer

The answer of Show that, given:  ...

Question 13

What advantages does the 2-factor Vasicek have when ﬁtting volatility?

Accepted Answer

Now the Vasicek model can bett

Question 14

In the 2-factor Hull-White model, what is the beneﬁt of introducing θt (time dependent central tendency)?

Accepted Answer

It provides two beneﬁts: First

Question 15

Why is it considered that implied volatility of interest rate options has a "hump" shape?

Accepted Answer

Because of mean reversion long

Question 16

Given that we now have two stochastic factors, when writing Ito's lemma as the following   what are we implicitly assuming about them?

Accepted Answer

We are assuming that

In the Vasicek one factor model, the short rate determines the model. In the Vasicek two factor model, what rates drive the model?

Under the Vasicek model, what degree of correlation do diﬀerent interest rates have?

When are multifactor models used?

How is the multivariate Ito's lemma deﬁned?

What are multifactor models?

What is the diﬀerence between using a model for ﬁnding arbitrage oppor- tunities and using a model for pricing derivatives and other securities?

Is the 2-factor Vasicek model an aﬁne model?

Can a solution always be found in order to price a security as proposed by the Feynman-Kac formula?

Does the 2-factor Vasicek model ﬁt the yield curve?

What peculiarity of a yield curve steepner makes the use of 2-factor models attractive?

What modi?cations should be included to Ito's lemma when we allow correlation between the two factors?

Show that, given:

What advantages does the 2-factor Vasicek have when ﬁtting volatility?

In the 2-factor Hull-White model, what is the beneﬁt of introducing θt (time dependent central tendency)?

Why is it considered that implied volatility of interest rate options has a "hump" shape?

Given that we now have two stochastic factors, when writing Ito's lemma as the following what are we implicitly assuming about them?

An Introduction to Fixed Income Markets

Basics of Fixed Income Securities

Basics of Interest Rate Risk Management

Basic Refinements in Interest Rate Risk Management

Interest Rate Derivatives: Forwards and Swaps

Interest Rate Derivatives: Futures and Options

Inflation, Monetary Policy, and the Federal Funds Rate

Basics of Residential Mortgage Backed Securities

One Step Binomial Trees

Multi-Step Binomial Trees

Risk Neutral Trees and Derivative Pricing

American Options

Monte Carlo Simulations on Trees

Interest Rate Models in Continuous Time

No Arbitrage and the Pricing of Interest Rate Securities

Dynamic Hedging and Relative Value Trades

Dynamic Hedging and Relative Value Trades

The Risk and Return of Interest Rate Securities

No Arbitrage Models and Standard Derivatives

The Market Model for Standard Derivatives

Forward Risk Neutral Pricing and the Libor Market Model

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Exam 22: Multifactor Models

In the Vasicek one factor model, the short rate determines the model. In the Vasicek two factor model, what rates drive the model?

Under the Vasicek model, what degree of correlation do diﬀerent interest rates have?

When are multifactor models used?

How is the multivariate Ito's lemma deﬁned?

What are multifactor models?

What is the diﬀerence between using a model for ﬁnding arbitrage oppor- tunities and using a model for pricing derivatives and other securities?

Is the 2-factor Vasicek model an aﬁne model?

Can a solution always be found in order to price a security as proposed by the Feynman-Kac formula?

Does the 2-factor Vasicek model ﬁt the yield curve?

What peculiarity of a yield curve steepner makes the use of 2-factor models attractive?

What modi?cations should be included to Ito's lemma when we allow correlation between the two factors?

Show that, given:

What advantages does the 2-factor Vasicek have when ﬁtting volatility?

In the 2-factor Hull-White model, what is the beneﬁt of introducing θt (time dependent central tendency)?

Why is it considered that implied volatility of interest rate options has a "hump" shape?

Given that we now have two stochastic factors, when writing Ito's lemma as the following what are we implicitly assuming about them?

An Introduction to Fixed Income Markets

Basics of Fixed Income Securities

Basics of Interest Rate Risk Management

Basic Refinements in Interest Rate Risk Management

Interest Rate Derivatives: Forwards and Swaps

Interest Rate Derivatives: Futures and Options

Inflation, Monetary Policy, and the Federal Funds Rate

Basics of Residential Mortgage Backed Securities

One Step Binomial Trees

Multi-Step Binomial Trees

Risk Neutral Trees and Derivative Pricing

American Options

Monte Carlo Simulations on Trees

Interest Rate Models in Continuous Time

No Arbitrage and the Pricing of Interest Rate Securities

Dynamic Hedging and Relative Value Trades

Dynamic Hedging and Relative Value Trades

The Risk and Return of Interest Rate Securities

No Arbitrage Models and Standard Derivatives

The Market Model for Standard Derivatives

Forward Risk Neutral Pricing and the Libor Market Model

Filters