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Question
What are two important implications of assuming that prices follow a geometric Brownian motion?Answer
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Related questions
Q:
Assume the following: LN(S) and LN(Q) have a correlation coefficient of -0.65, S(0) = 55, Q(0) = 60, r = 0.04, σs = 0.22 σQ = 0.15, and dividends = 0. Using formula 20.39, what is the price of a claim that pays Q/?
A) $8.16
B) $9.16
C) $10.16
D) $11.16
Q:
Assume the following: LN(S) and LN(Q) have a correlation coefficient of 0.40, S(0) = 60, Q(0) = 60, r = 0.05, σs = 0.30 σQ = 0.25, and dividend = 0. Using formula 20.39, what is the price of a claim that pays ?
A) $243.96
B) $322.96
C) $479.96
D) $532.96
Q:
What advantage does a variance reduction technique offer?
Q:
Why are covariances and correlations relevant to simulation development?
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:
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:
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:
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:
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:
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 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 Nikkei index is 22,550, K = 21,000, σ = 0.19, rf = 0.04, S = 0.10, r = 0.08 and
div = 0.01. The yen to dollar spot rate is 104 and the correlation coefficient is 0.30. What would be the dollar price of a 2-year equity-linked foreign exchange call?
A) $45.02
B) $35.02
C) $25.01
D) $15.02
Q:
The current Nikkei index price is 21,200. Assume σ = 0.13, r = 0.05 and div = 0.015. If
K = 20,000 yen and yen per dollar spot rates are 103, what is the dollar value of a 2-year call?
A) $13.97
B) $18.97
C) $23.97
D) $28.97
Q:
The Buckingham Casino offers to give every gambler one share of Buckingham Casino Corp. stock if the price drops below $40.00, as an incentive to spur business. If S = $45.25, σ = 0.15,
r = 0.05 and div = 0, how much profit or loss is Buckingham incurring if they charge $0.25 to participate in this wager?
A) $0.31 loss
B) $0.31 profit
C) $0.19 loss
D) $0.19 profit
Q:
In a specific wager, Pat is paid $5.00 if the price of ABC Corp. is above $85.00. Currently, ABC Corp. price is $75.00, σ = 0.25, r = 0.04, div = 0 and the wager lasts 6 months. If the price is below $85.00, Pat must pay $5.00. What is the net value of Pat's wager?
A) -$2.49
B) +$2.49
C) -$1.50
D) +$1.50
Q:
What does Girsanov's theorem tell us about drift and Brownian motion?
Q:
For a utility function that exhibits decreasing martingale utility, the martingale utility is high when:
A) Consumption and utility are low
B) Consumption and utility are high
C) Consumption is low and utility is high
D) Consumption is high and utility is low
Q:
Briefly define a terminal boundary condition.
Q:
Mary wagers to pay one share of stock to Matt if the price at expiration in 1 year is above $75.00. Assume S(0) = 60.00, σ = 0.15, r = 0.04, and dividend rate = 0.01. What is the value of Mary's bet?
A) $6.55
B) $7.55
C) $8.55
D) $9.55
Q:
What is the relationship of the Sharpe ratios and risk premiums between stocks and options?
Q:
When hedging a foreign currency position, what makes a down-and-out put unattractive?
Q:
Assume S = $42, K = 45, div = 0, r = 0.04, σ = 0.48, and 80 days until expiration. What is the premium on a knock-out put option with a down-and-out barrier of $44?
A) $2.13
B) $3.13
C) $3.47
D) $4.07
Q:
What is the payoff on a 75 strike Asian option given it is a geometric average price call? The recent prices are 72, 76, 74, 78, and 78.
A) 0.46
B) 0.56
C) 0.66
D) 0.76
Q:
Assume S = $33.00, σ = 0.32, r = 0.06, div = 0.01, on a $35 strike call. Given delta = 0.3854 and gamma = 0.0847, what is the delta-gamma approximation for the call price on a $0.50 stock price increase? Assume 68 days until expiration.
A) $1.34
B) $1.36
C) $1.38
D) $1.40
Q:
What is the total dollar cost to create a delta hedge position against a 200 short call position? Assume calls are priced at $4.16, the delta is 0.7644, and stock price is $73.00.
A) $9,880
B) $10,328
C) $11,168
D) $12,660
Q:
What actions are required to both delta-hedge and gamma-hedge a written option position?