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Question
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.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:
What are two important implications of assuming that prices follow a geometric Brownian motion?
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