Question 1

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

Accepted Answer

The larger the number of draws,the better the results.

Question 2

What advantage does a variance reduction technique offer?

Accepted Answer

When repeated Monte Carlo simulations are performed,techniques exist to increase the efficiency of the simulations and identify better fitting distributions.

Question 3

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

Accepted Answer

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

Question 4

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

Accepted Answer

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

Question 5

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?

Accepted Answer

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

Question 6

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

Accepted Answer

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

Question 7

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

Accepted Answer

Since an Asian option uses the

Question 8

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

Accepted Answer

An estimate of the error in ea

Question 9

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

Accepted Answer

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

Question 10

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?

Accepted Answer

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

Question 11

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

Accepted Answer

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

Question 12

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

Accepted Answer

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

Question 13

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

Accepted Answer

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

Question 14

Why are covariances and correlations relevant to simulation development?

Accepted Answer

Stocks often move together to

Question 15

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

Accepted Answer

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

Question 16

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

Accepted Answer

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

Question 17

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

Accepted Answer

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

Question 18

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.

Accepted Answer

Simulations can be used to improve prici

Question 19

Monte Carlo simulation assumes all assets earn:

Accepted Answer

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

Question 20

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

Accepted Answer

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

Exam 19: Monte Carlo Valuation

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

What advantage does a variance reduction technique offer?

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

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

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?

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

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

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

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

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?

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

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

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

Why are covariances and correlations relevant to simulation development?

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

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

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

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.

Monte Carlo simulation assumes all assets earn:

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

Introduction to Derivatives

An Introduction to Forwards and Options

Insurance, collars, and Other Strategies

Introduction to Risk Management

Financial Forwards and Futures

Commodity Forwards and Futures

Interest Rate Forwards and Futures

Swaps

Parity and Other Option Relationships

Binomial Option Pricing: Basic Concepts

Binomial Option Pricing: Selected Topics

The Black-Scholes Formula

Market-Making and Delta-Hedging

Exotic Options: I

Financial Engineering and Security Design

Corporate Applications

Real Options

The Lognormal Distribution

Brownian Motion and Itos Lemma

The Black-Scholes-Merton Equation

Risk-Neutral and Martingale Pricing

Exotic Options: 2

Volatility

Interest Rate and Bond Derivatives

Value at Risk

Credit Risk

Filters