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Q:
Why are covariances and correlations relevant to simulation development?
Q:
How does a control variate method make a naive Monte Carlo more efficient?
Q:
Why does an Asian option benefit from a larger number of draws in a Monte Carlo simulation?
Q:
How does the number of draws impact the validity of a Monte Carlo simulation?
Q:
If using Monte Carlo simulation, what is a typical number of iterations employed in the model?A) 1B) 10C) 1,000D) 1,000,000
Q:
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
Q:
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%
Q:
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
Q:
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
Q:
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
Q:
Which of the following options would not benefit from using a Monte Carlo simulation?
A) American
B) Asian
C) European
D) Barrier
Q:
What statistic is used to determine the accuracy of a Monte Carlo simulation?
A) Mean
B) Standard deviation
C) Covariance
D) Correlation coefficient
Q:
In what option does it benefit to simulate the path of potential asset prices?
A) Barrier
B) European
C) Asian
D) A and C
Q:
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
Q:
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
Q:
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
Q:
Monte Carlo simulation assumes all assets earn:
A) Risk-free rate
B) Market Index return
C) YTM on AAA Bonds
D) Brokers call
Q:
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
Q:
Why do we assume a lognormal distribution in option pricing?
Q:
How are partial expectation prices converted to conditional expectation prices?
Q:
Why might normally distributed returns appear non-normal?
Q:
What assumption is made in the Black-Scholes model concerning volatility?
Q:
In a lognormal model of stock price movement, describe the mean and variance of the continuously compounded returns.
Q:
Give a very brief definition of conditional expected stock price.
Q:
A stock is valued at $28.00. The annual expected return is 9.0% and the standard deviation of annualized returns is 19.0%. If the stock is lognormally distributed, what is the price of the stock given a one standard deviation move up after 4 years?A) $28.00B) $32.33C) $40.13D) $54.60
Q:
A stock is valued at $28.00. The annual expected return is 9.0% and the standard deviation of annualized returns is 19.0%. If the stock is lognormally distributed, what is the expected median stock price after 4 years?
A) $28.00
B) $32.33
C) $40.13
D) $54.60
Q:
A stock is valued at $28.00. The annual expected return is 9.0% and the standard deviation of annualized returns is 19.0%. If the stock is lognormally distributed, what is the expected price after 4 years?
A) $28.00
B) $32.33
C) $40.13
D) $54.60
Q:
A stock is valued at $55.00. The annual expected return is 12.0% and the standard deviation of annualized returns is 22.0%. If the stock is lognormally distributed, what is the price of the stock given a one standard deviation move up after 3 years?
A) $64.41
B) $74.41
C) $84.41
D) $94.41
Q:
A stock is valued at $55.00. The annual expected return is 12.0% and the standard deviation of annualized returns is 22.0%. If the stock is lognormally distributed, what is the expected median stock price after 3 years?
A) $57.67
B) $67.67
C) $77.67
D) $87.67
Q:
A stock is valued at $55.00. The annual expected return is 12.0% and the standard deviation of annualized returns is 22.0%. If the stock is lognormally distributed, what is the expected price after 3 years?
A) $78.83
B) $88.83
C) $98.83
D) $108.83
Q:
For a stock price that was initially $55.00, what is the price after 4 years if the continuously compounded returns for these 4 years are 4.5%, 6.2%, 8.9%, -3.2%?
A) $64.80
B) $74.80
C) $84.80
D) $94.80
Q:
Given a mean of 45 and a standard deviation of 32 from a normally distributed sample, what is the probability of an observation being between 35 and 75?
A) 0.35
B) 0.45
C) 0.55
D) 0.65
Q:
Given a mean of -7.8 and a standard deviation of 16 from a normally distributed sample, what is the probability of an observation being below 12.0?
A) 0.51
B) 0.61
C) 0.71
D) 0.81
Q:
Given a mean of -4.3 and a standard deviation of 26, what is the equivalent draw from a normal distribution for a standard normal sample variable of 0.67?
A) -13.12
B) 03.12
C) 13.12
D) 23.12
Q:
Given a mean of 4.5 and a standard deviation of 12 from a sample of variables, what is the equivalent draw from a standard normal distribution for 6.0?
A) 0.065
B) 0.075
C) 0.095
D) 0.125
Q:
What is the probability that a number drawn from the standard normal distribution will NOT be between -1 and 1?
A) 0.22
B) 0.32
C) 0.42
D) 0.52
Q:
What is the probability that a number drawn from the standard normal distribution will be between -0.60 and 0.45?
A) 0.40
B) 0.50
C) 0.60
D) 0.70
Q:
What is the area under the standard normal distribution curve and is less than 0.654?
A) 0.5115
B) 0.6215
C) 0.7434
D) 0.8283
Q:
How are call and put options used to value starting, stopping, and restarting commodity extraction projects?
Q:
What two components go into valuing an infinite commodity reserve?
Q:
In the context of peak-load energy generation and a European exchange option, what is the spark spread?
Q:
What is the main difference in pricing R & D options versus most other real options?
Q:
Why is the perpetual call formula used to price commodity extraction options?
Q:
What is the relationship, in general, between volatility and trigger prices, assuming constant costs?
Q:
An existing well is operating and the price of oil is $115 per barrel. The effective lease rate and risk free rate are 3.0% and 4.0%, respectively. The constant cost of extraction is $85 per barrel and the volatility of prices is 15.0%. If it costs nothing to shut down the well, at what price would we close the well?A) $41B) $48C) $52D) $59
Q:
The price of oil is $115 per barrel. The effective lease rate and risk free rate are 3.0% and 4.0%, respectively. The constant cost of extraction is $85 per barrel and the volatility of prices is 15.0%. If an untapped well costs $2,100 to open and can produce indefinitely, at what price per barrel should the well be opened?
A) $349
B) $423
C) $454
D) $484
Q:
The price of oil is $115 per barrel. The effective lease rate and risk free rate are 3.0% and 4.0%, respectively. The constant cost of extraction is $85 per barrel and the volatility of prices is 15.0%. If an untapped well costs $2,100 to open and can produce indefinitely, what is the value of the unopened well?
A) $724
B) $854
C) $913
D) $1,025
Q:
The price of oil is $120 per barrel. The effective lease rate and risk free rate are 5.0% and 6.0%, respectively. The constant cost of extraction is $105 per barrel and the volatility of prices is 18.0%. What is the value of an option to defer extraction?
A) $30.68
B) $32.08
C) $34.56
D) $38.34
Q:
The current price of silver is $32.00 per ounce. The effective lease rate and risk free rate are 3.0% and 4.0%, respectively. If the cost to mine one ounce of silver is a constant $25.00, what is the trigger price per ounce at which the silver will be mined?
A) $33.17
B) $35.17
C) $37.17
D) $39.17
Q:
The current price of silver is $ 31.00 per ounce. The effective lease rate and risk free rate are 1.0% and 3.5%, respectively. If the cost to mine one ounce of silver is a constant $25.00, what is the value of an option to wait and mine the silver later?
A) $13.50
B) $14.50
C) $15.50
D) $16.50
Q:
The current price per ton of iron ore is $145.00. The effective lease rate is 3.0% and the risk free rate is 4.5%. The cost to mine one ton of iron ore is $110.00 and constant. What is the trigger price at which we will mine the iron ore?
A) $163.80
B) $180.40
C) $210.50
D) $205.70
Q:
The current price per cord of lumber is $26.00. The effective annual lease rate is 2.0% and the risk free rate is 4.0%. The cost to harvest one cord is $20.00 and constant. What is the trigger price at which we will harvest the lumber?
A) $27.61
B) $31.61
C) $35.61
D) $39.61
Q:
Use a binomial tree to value to following option. Assume rf = 0.045, rp = 0.14, σ = 0.20, E(CF1) = $62 million, g = 0.03, time horizon = 2 years, binomial period = 1 year, and
cost = $500 million. What is the value of this project option?
A) $47 million
B) $57 million
C) $67 million
D) $77 million
Q:
Use Cox-Ross-Rubenstein to construct a 2-year binomial tree for the evolution of cash flows with a binomial period of 1. Assume the initial cash flow is (CF1) = $62 million, σ = 0.20,
rp = 0.14, and g = 0.03. What is the highest possible value of the project?
A) $222 million
B) $314 million
C) $622 million
D) $841 million
Q:
Use a binomial tree to value the following option. Assume rf = 0.04, rp =0.12, σ = 0.35, E(CF1) = $30, and cost = $300. What is the value of this project option?
A) $40.74
B) $50.60
C) $55.32
D) $62.12
Q:
Use Cox-Ross-Rubenstein to construct a 2-year binomial tree for the evolution of cash flows with a binomial period of 1. Assume the initial cash flow (CF1) is $20 million, σ = 0.45, r = 0.13, g = 0.02, and the project lasts 2 years. What is the value of the project on the up node in year 1?
A) $85 million
B) $185 million
C) $285 million
D) $385 million
Q:
Walla, Inc. may invest $6 million in a Buffalo harvesting project. Annual costs and revenues, starting next year, are forecasted to be $1 million and $0.7 million, growing at 0.0% and 3.0%, respectively. If the opportunity cost of capital is 4.5%, what is the investment trigger price?
A) $19.25 million
B) $21.25 million
C) $23.25 million
D) $25.25 million
Q:
Geek Is Us, Inc. may invest $8 million in an Alien Spectograph project. Annual costs and revenues, starting next year, are forecasted to be $3 million and $2 million growing at 0.0% and 4.0%, respectively. If the opportunity cost of capital is 6.0% and σ = 0.0, what is the investment trigger price?
A) $20.95 million
B) $30.95 million
C) $40.95 million
D) $50.95 million
Q:
Techie, Inc. may invest $5 million in a new Star Communicator project. Annual production costs and revenues are projected to be $2 million and $1.5 million, with each growing at 2.0% and 4.0%, respectively. At an interest rate of 5.5%, what is the approximate investment year that will maximize value? (Use static analysis.)
A) Year 20
B) Year 15
C) Year 10
D) Year 5
Q:
Mead, Inc. may invest $20 million in a new fiber optic project. Due to market conditions, annual production costs and revenues are forecasted at $10 million and $8 million, respectively, starting next year. Revenues are expected to grow at 4.0% and interest rates are 6.0%. What is the change in value if the project is commenced in 5 years instead of today? (Use static analysis.)
A) $8.84 million
B) $10.84 million
C) $12.84 million
D) $14.84 million
Q:
Why should or should not a company expense compensation options?
Q:
The use of collars in acquisitions serves the purpose of addressing what two issues in an offer?
Q:
What three components exist in the value of an "outperform stock option"?
Q:
What feature of reload options prevents the use of a Black-Scholes valuation?
Q:
Why does a company sell a put when issuing compensation options?
Q:
How does a reload option provide additional compensation compared to regular compensation options?
Q:
In the case of an acquisition, with which of the following offer structures does the acquired firm bear the most risk between the time the offer is accepted and the time it is consummated?A) Fixed stock offerB) Floating stock offerC) Fixed collar offerD) Floating collar offer
Q:
A company issues an option grant with an outperformance feature, against the S&P 500. Assume S&P 500 = 1100, S = 46, k = 45, σ = 0.30, r = 0.04, and 10 years until expiration. The S&P 500 has a dividend yield of 2.5%, standard deviation of 20.0% and a 0.45 correlation coefficient with the stock. What is the value of the outperformance feature?
A) $2.25
B) $3.29
C) $4.11
D) $4.78
Q:
A company issues an option grant with an outperformance feature, against the S&P 500. Assume S&P 500 = 1100, S = 46, k = 45, σ = 0.30, r = 0.04, and 10 years until expiration. The S&P 500 has a dividend yield of 2.5%, standard deviation of 20.0% and a 0.45 correlation coefficient with the stock. What is the value of the outperformance option?
A) $11.92
B) $15.99
C) $19.75
D) $21.05
Q:
A company issues an option grant with an outperformance feature, against the S&P 500. Assume S&P 500 = 950, S = 22, k = 25, σ = 0.25, r = 0.06, and 5 years until expiration. The S&P 500 has a dividend yield of 2%, standard deviation of 18.0% and a 0.30 correlation coefficient with the stock. What is the value of the outperformance feature?
A) $0.99
B) $1.31
C) $1.59
D) $1.72
Q:
Lechno, Inc. issues compensation options with the following terms. Strike = $65,
price = $63.50, σ = 0.22, r = 0.045, div = 0.015. What is the value of the option if it will be repriced at $40? Assume 10 years to expiration.
A) $18.64
B) $22.22
C) $24.32
D) $26.84
Q:
Willco, Inc. issues compensation options with the following terms. Strike = $45,
price = $42.00, σ = 0.48, r = 0.05, div = 0.02. What is the value of the option if it will be
repriced at $30? Assume 10 years to expiration.
A) $22.78
B) $24.65
C) $26.22
D) $30.46
Q:
Daniels, Inc. has assets valued at $2 million and 50,000 outstanding shares. A 5-year zero-coupon bond exists, which pays $400,000 at maturity. The bond is convertible into 10,000 shares. Assume σ = 0.30, r = 0.055, and no dividend is paid. What is the value of the bond?
A) $402,672
B) $452,172
C) $415,022
D) $385,172
Q:
James, Inc. has zero-coupon outstanding debt maturing in 8 years. In rank of seniority, each pays at maturity $20 million, $15 million, and $40 million. Assume asset value = $60 million,
r = 0.05, σ = 0.28, and no dividend is paid. What is the yield on the $15 million subordinate debt?
A) 5.72%
B) 6.72%
C) 7.72%
D) 8.72%
Q:
What is the difference in the expected returns on equity when using a Black-Scholes formula versus a traditional weighted average formula? Assume rA = 0.12, rf = 0.06, asset value = $170, equity value = $45, debt to value ratio = 0.55, and delta = 0.6500.
A) 1.00%
B) 1.20%
C) 1.40%
D) 1.60%
Q:
What is the expected return on equity using the Black-Scholes formula, given a zero-coupon bond that pays $250 at maturity in 4 years? Assume assets are worth $200, r = 0.05, σ = 0.30, and no dividend is paid. The return on assets is 11.5%.
A) 10.27%
B) 14.27%
C) 18.27%
D) 22.27%
Q:
Compute the yield on debt given a 10-year zero-coupon bond paying $500 at maturity. Assume the asset value is $450, σ = 0.35, r = 0.06, and no dividend is paid.
A) 6.62%
B) 7.26%
C) 8.26%
D) 9.62%
Q:
Jessie, Inc. has 4-year zero-coupon bonds outstanding, which will pay $1,000 at maturity. The assets are valued at $900, σ = 0.25, r = 0.045, and the company does not pay a dividend. Using a Black-Scholes model, what is the yield on debt?
A) 4.68%
B) 6.48%
C) 8.46%
D) 8.64%
Q:
We will assume that Nathans, Inc. has 3-year zero-coupon debt outstanding, which will pay $200 at maturity. The assets are valued at $175, σ = 0.20, r = 0.04, and the company does not pay a dividend. Using a Black-Scholes model, what is the value of the equity?
A) $23.05
B) $43.05
C) $63.05
D) $83.05
Q:
The chapter discusses the merging of debt and options. Ask the class why firms would consider such instruments. Highlight the use of a PERC by a company that has difficulty issuing debt, yet can offer the carrot of price appreciation.