Deck 13: Monte Carlo Simulations on Trees

Question 1

What is a standard error?

Answer 1

Standard error is the standard deviation of an estimate (e.g. the ones obtained through Monte Carlo Simuations). It is defined as SE = σ/√N.

Question 2

What is a prepayment model?

Answer 2

A prepayment model is a model that predicts the amount of prepayment to occur under different market conditions. It may include the factors mentioned before (random events, seasonality and forgetfulness) as well as others.

Question 3

What is a Monte Carlo Simulation?

Answer 3

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

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

Question 5

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

Question 6

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

Question 7

How is spot rate duration defined in Monte Carlo simulations?

Question 8

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

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.

Question 10

What is a confidence interval?

Question 11

What additional factors may affect the prepayment decision?

Question 12

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

Question 13

What is an Asian Interest Rate Option?

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?

Question 15

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

Question 16

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?

Question 17

How many simulations are enough?

Question 18

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