Deck 19: Monte Carlo Valuation

Question 1

Which of the following options would not benefit from using a Monte Carlo simulation?

A) American
B) Asian
C) European
D) Barrier

Answer 1

C

Question 2

Which distribution is a discrete probability distribution that counts the number of events,such as large stock price moves,that occur over a period of time?

A) Latin hypercube
B) Normal
C) Lognormal
D) Poisson

Answer 2

D

Question 3

When a stock price movement occurs and is more than we would expect from a lognormal distribution,we refer to this as:

A) Pull
B) Jump
C) Squat
D) Push

Answer 3

B

Question 4

What advantage does a variance reduction technique offer?

Question 5

What type of random variable is necessary for a Monte Carlo valuation?

A) Standard normal distribution
B) Normal distribution
C) Lognormal distribution
D) All of the above

Question 6

What technique might be used to improve the accuracy of a Monte Carlo simulated output?

A) Arithmetic Asian option
B) Control variate method
C) Poisson Distribution with jumps
D) Risk neutral probabilities

Question 7

Monte Carlo simulation assumes all assets earn:

A) Risk-free rate
B) Market Index return
C) YTM on AAA Bonds
D) Brokers call

Question 8

When valuing options using true probabilities,the discount rate is computed as follows:

A) Once using the risk-free rate
B) At the final period
C) For each node
D) For each path

Question 9

In what option does it benefit to simulate the path of potential asset prices?

A) Barrier
B) European
C) Asian
D) A and C

Question 10

Why are covariances and correlations relevant to simulation development?

Question 11

Given X₁ = N (0,1)and X₂ = N (0.5,8),what is the mean of eˣ²?

A) 69.97
B) 79.97
C) 89.97
D) 99.97

Question 12

How does a control variate method make a naive Monte Carlo more efficient?

Question 13

Why does an Asian option benefit from a larger number of draws in a Monte Carlo simulation?

Question 14

A critical assumption in Monte Carlo simulations is that valuation is based on:

A) Random variables
B) True probabilities
C) Risk-neutral probabilities
D) None of the above

Question 15

If using Monte Carlo simulation,what is a typical number of iterations employed in the model?

A) 1
B) 10
C) 1,000
D) 1,000,000

Question 16

How does the number of draws impact the validity of a Monte Carlo simulation?

Question 17

Ask the class to state how simulations could be used to improve pricing models.Highlight situations where historical results violated pricing assumptions and how simulations may have provided better results.

Question 18

What method uses the insight that for each simulated realization there is an opposite and equally likely realization?

A) Stratified sampling
B) Control variate
C) Antithetic variate
D) Efficient variate

Question 19

What statistic is used to determine the accuracy of a Monte Carlo simulation?

A) Mean
B) Standard deviation
C) Covariance
D) Correlation coefficient

Question 20

A stock owned by a portfolio has a bankruptcy probability of 1% per year.Using a Poisson distribution,what is the probability that this firm will not declare bankruptcy over the upcoming 10 years?

A) 60%
B) 70%
C) 80%
D) 90%