Question 1

Why is it useful to price Mortgage Backed Securities (MBS) through Monte Carlo Simulations?

Accepted Answer

Because we can incorporate additional factors aﬀecting the prepayment decision into the pricing model.

Question 2

What additional factors may aﬀect the prepayment decision?

Accepted Answer

Some additional factors aﬀecting the prepayment decision are: i. Random Event. For example the sale of the house. ii. Seasonality. Homeowners tend to move much more over the summer than in the winter. iii. Forgetfulness. Some homeowners don't pay attention to the fact that interest rates are suﬃcently low to reﬁnance their mortgage.

Question 3

What is a Monte Carlo Simulation?

Accepted Answer

A Monte Carlo Simulation is a methodology of predicting the behavior of a variable by simulating a large number of paths under which the random component of the variable can take any value. The result is a large sample of possible values for the variable from which we can infer its expected value and other moments.

Question 4

When pricing through Monte Carlo simulations on trees we are implic- itly using risk neutral probabilities, this is also so when computing the spot rate duration. Is this correct? Shouldn't measures of sensitivity be computed with risk natural probabilities?

Accepted Answer

No, when we review the spot rate duratio

Question 5

How is spot rate duration deﬁned in Monte Carlo simulations?

Accepted Answer

Spot rate

Question 6

What is a standard error?

Accepted Answer

Standard error is the standard

Question 7

Is the traditional tree methodology well-suited to price the following: a ﬁxed-for-ﬂoating swap where LIBOR is the underlying rate.

Accepted Answer

Yes, tress can price

Question 8

Given that simulations do not oﬀer a closed form solution, can we still calculate a price's sensitivity to interest rate movements?

Accepted Answer

Yes, we can still do so throug

Question 9

Is the traditional tree methodology well-suited to price the following: an option where the owner has the right to buy a bond at its lowest price over some speciﬁed period.

Accepted Answer

No, this security, called a "l

Question 10

What is a prepayment model?

Accepted Answer

A prepayment model is a model that predi

Question 11

How eﬀective is pricing of Collateralized Mortgage Obligations (CMO) on a risk neutral tree? Why?

Accepted Answer

The tree methodology has many

Question 12

What is an Asian Interest Rate Option?

Accepted Answer

An Asian Interest Ra

Question 13

In the context of the prepayment of mortgages, what is seasonality?

Accepted Answer

Seasonaility is a factor that

Question 14

When pricing zero coupon bonds, are results from the Monte Carlo simu- lations on a tree the same as risk neutral pricing on a tree? Why?

Accepted Answer

They might not be th

Question 15

What advantages do Monte Carlo simulatons on a tree provide when pric- ing MBS tranches?

Accepted Answer

Through Monte Carlo simulations we can a

Question 16

How many simulations are enough?

Accepted Answer

As many as we need t

Question 17

What is a conﬁdence interval?

Accepted Answer

A conﬁdence interval presents

Question 18

How does seasonality aﬀect the prepayment option? Is the link direct?

Accepted Answer

This factor does not aﬀect the decision

Why is it useful to price Mortgage Backed Securities (MBS) through Monte Carlo Simulations?

What additional factors may aﬀect the prepayment decision?

What is a Monte Carlo Simulation?

When pricing through Monte Carlo simulations on trees we are implic- itly using risk neutral probabilities, this is also so when computing the spot rate duration. Is this correct? Shouldn't measures of sensitivity be computed with risk natural probabilities?

How is spot rate duration deﬁned in Monte Carlo simulations?

What is a standard error?

Is the traditional tree methodology well-suited to price the following: a ﬁxed-for-ﬂoating swap where LIBOR is the underlying rate.

Given that simulations do not oﬀer a closed form solution, can we still calculate a price's sensitivity to interest rate movements?

Is the traditional tree methodology well-suited to price the following: an option where the owner has the right to buy a bond at its lowest price over some speciﬁed period.

What is a prepayment model?

How eﬀective is pricing of Collateralized Mortgage Obligations (CMO) on a risk neutral tree? Why?

What is an Asian Interest Rate Option?

In the context of the prepayment of mortgages, what is seasonality?

When pricing zero coupon bonds, are results from the Monte Carlo simu- lations on a tree the same as risk neutral pricing on a tree? Why?

What advantages do Monte Carlo simulatons on a tree provide when pric- ing MBS tranches?

How many simulations are enough?

What is a conﬁdence interval?

How does seasonality aﬀect the prepayment option? Is the link direct?

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

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

Multifactor Models

Filters

Exam 13: Monte Carlo Simulations on Trees

Why is it useful to price Mortgage Backed Securities (MBS) through Monte Carlo Simulations?

What additional factors may aﬀect the prepayment decision?

What is a Monte Carlo Simulation?

When pricing through Monte Carlo simulations on trees we are implic- itly using risk neutral probabilities, this is also so when computing the spot rate duration. Is this correct? Shouldn't measures of sensitivity be computed with risk natural probabilities?

How is spot rate duration deﬁned in Monte Carlo simulations?

What is a standard error?

Is the traditional tree methodology well-suited to price the following: a ﬁxed-for-ﬂoating swap where LIBOR is the underlying rate.

Given that simulations do not oﬀer a closed form solution, can we still calculate a price's sensitivity to interest rate movements?

Is the traditional tree methodology well-suited to price the following: an option where the owner has the right to buy a bond at its lowest price over some speciﬁed period.

What is a prepayment model?

How eﬀective is pricing of Collateralized Mortgage Obligations (CMO) on a risk neutral tree? Why?

What is an Asian Interest Rate Option?

In the context of the prepayment of mortgages, what is seasonality?

When pricing zero coupon bonds, are results from the Monte Carlo simu- lations on a tree the same as risk neutral pricing on a tree? Why?

What advantages do Monte Carlo simulatons on a tree provide when pric- ing MBS tranches?

How many simulations are enough?

What is a conﬁdence interval?

How does seasonality aﬀect the prepayment option? Is the link direct?

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

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

Multifactor Models

Filters