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Q:
What is the primary difference between an equity-linked bond and a currency-linked bond?
Q:
How does a coupon bond differ from an equity-linked bond?
Q:
What possible tax advantage exists in equity-linked notes?
Q:
Instead of issuing a pure commodity-linked debt, why would the commodity producing firm consider a combining interest plus participation in the commodity price appreciation?
Q:
For whom would the issue of an oil-linked debt instrument not be considered a risky issue?
Q:
Which of the following financially engineered products is NOT used to defer the payment of capital gains taxes on securities that have appreciated?A) Commodity Linked OptionsB) DECSC) Equity Linked NotesD) PEPS
Q:
A commodity linked bond is issued with an embedded call option. The current commodity price is $52, as is the exercise price on the call option. The call option is priced at $5.56. If the promised payment on the bond is the same as the issue price of $40, what is the yield on the bond if effective interest rates are 4.0% and the bond has a 1-year maturity?
A) 2.24%
B) 2.80%
C) 3.50%
D) 4.0%
Q:
A commodity linked bond is issued with an embedded call option. The current commodity price is $110, as is the exercise price on the call option. The call option is priced at $3.41. If the promised payment on the bond is the same as the issue price of $100, what is the implied coupon if effective interest rates are 3.0% and the bond has a 1-year maturity?
A) $0.66
B) $0.77
C) $0.88
D) $0.99
Q:
We wish to cap participation in a 3-year equity-linked option at 50.0% return. Our profit alpha is 3.0%. The S&P 500 price = 950, div = 0.015, σ = 0.22, and interest rates are 4.8%. What is the implied participation rate?
A) 0.66
B) 0.76
C) 0.96
D) 1.16
Q:
What is the price of a 2-year equity-linked CD under the following terms? No coupon is paid. At maturity the CD pays 80.0% of the S&P 500 index appreciation. The S&P 500 price = 900, div = 0.02, σ = 0.20, and interest rates are 5.0%.A) $890.22B) $990.23C) $1064.20D) $1110.55
Q:
Assume the price of Mary, Inc. stock is $56.00, interest rates are 4.8%, div yield = 0, and
σ = 0.35. What is the price of a $1,000 par value 2-year price-participation note paying a 5.0% annual coupon and receiving 50.0% of all price appreciation above $65.00?
A) $896.44
B) $996.44
C) $1006.44
D) $1106.44
Q:
Assume oil prices rise dramatically and the spot price of oil is $230 per barrel and the 3-year forward price is $245. Annualized 1-year, 2-year, and 3 year interest rates are 4.2%, 4.4%, and 4.6%, respectively. For a commodity-linked note to sell at par, what is the annual coupon?
A) $6.00
B) $16.00
C) $26.00
D) $36.00
Q:
Assume the spot price of gold is $745 per ounce and the 2-year forward price is $773. Annualized 1-year and 2-year forward interest rates are 5.0% and 5.2%, respectively. For a commodity-linked note to sell at par, what is the annual coupon?
A) $23.09
B) $24.09
C) $25.09
D) $26.09
Q:
Assume the spot price of gold is $750 per ounce, the 1-year forward price is $770, and the annual interest rate is 4.5%. What is the price of a zero-coupon note paying 1 ounce of gold in one year?
A) $770
B) $750
C) $725
D) $736
Q:
Will, Inc. stock is $63.35 per share. The company's quarterly dividend is forecasted as $0.10 per share, increasing 5.0% every quarter. A coupon equity-linked bond, promising to pay one share of Will, Inc. in 2 years pays a semi-annual coupon of $0.20. If annualized interest rates are 8.0%, what is the price of the bond?
A) $59.55
B) $61.14
C) $63.12
D) $65.22
Q:
Wayne, Inc. stock is $40.00 per share. The company's quarterly dividend is forecasted as $0.45 per share, indefinitely. A coupon equity-linked bond, promising to pay one share of Wayne, Inc. in 3 years pays a quarterly coupon of $0.50. If annual interest rates are 4.0%, what is the price of the bond?
A) $40.56
B) $42.60
C) $44.56
D) $46.60
Q:
Dawn, Inc. stock is $37.00 per share. The company's semi-annual dividend is forecasted as $0.25 per share, increasing every 6 months by 20.0%. What is the price of a zero-coupon equity-linked bond, promising to pay one share in 4 years, given annual interest rates of 6.0%?
A) $32.29
B) $33.49
C) $34.39
D) $35.69
Q:
Albert, Inc. stock is $42.00 per share. The company's quarterly dividend is forecasted as $0.50 per share, increasing 10.0% at the start of every year. What is the price of a zero-coupon equity-linked bond, promising to pay one share in 3 years, given annual interest rates of 8.0%?
A) $32.60
B) $36.20
C) $42.60
D) $62.40
Q:
Mel, Inc. stock is $135.00 per share. The company's semi-annual dividend is forecasted as $2.10 per share, indefinitely. What is the price of a zero-coupon equity-linked bond, promising to pay one share in 3 years, given annual interest rates of 5.0%?
A) $101.35
B) $110.26
C) $123.45
D) $155.22
Q:
Why are exotic options not so exotic?
Q:
What is the primary difference between a standard option and an exchange option?
Q:
For a long put position, what benefit is provided by a gap option should prices rise?
Q:
Why is the premium on a standard option and down-and-in call the same when the barrier price exceeds the stock price?
Q:
When hedging a foreign currency position, what makes a down-and-out put unattractive?
Q:
Why might a down-and-in put option be more attractive than a standard option when hedging a foreign currency position?
Q:
The underlying stock for a European exchange option has S = $27.15, div = 2.0%, andσ = 0.18. The strike stock has S = $30.00, div = 0.0%, and σ = 0.22. The two stocks have a correlation coefficient of 0.73. If the exchange option expires in 2 years, what is the price of the call using a Black-Scholes approach?A) $0.88B) $0.98C) $1.09D) $1.19
Q:
Assume S = $31.75, div = 0, r = 0.03, and σ = 0.20, and 90 days until the expiration of a standard call option. A put on call compound option with an exercise price of $2.00 has 180 days until expiration. What is the premium of the put on call option?
A) $0.42
B) $0.48
C) $0.85
D) $1.11
Q:
Assume S = $31.75, div = 0, r = 0.03, and σ = 0.20, and 90 days until the expiration of a standard call option. A call on call compound option with an exercise price of $2.00 has 180 days until expiration. What is the premium of the call on call option?
A) $1.46
B) $2.46
C) $3.04
D) $3.53
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:
Assume S = $46, K = 45, div = 0, r = 0.03, σ = 0.20, and 50 days until expiration. What is the premium on a knock-out put option with an up-and-out barrier of $50?
A) $0.83
B) $0.93
C) $1.13
D) $1.33
Q:
Assume S = $66, K = 65, div = 0, r = 0.04, σ = 0.25, and 60 days until expiration. What is the premium on a knock-out call option with a down-and-out barrier of $60?
A) $2.40
B) $2.70
C) $3.00
D) $3.30
Q:
Assume S = $53, K = 50, div = 0, r = 0.03, σ = 0.30, and 100 days until expiration. What is the premium on a knock-in put option with an up-and-in barrier of $55?
A) $0.63
B) $0.73
C) $0.83
D) $0.93
Q:
Assume S = $63, K = 60, div = 0, r = 0.04, σ = 0.35, and 90 days until expiration. What is the premium on a knock-in call option with an up-and-in barrier of $65?
A) $1.96
B) $2.06
C) $2.16
D) $2.26
Q:
Assume S = $51, K = $50, div = 0.0, r = 0.05, σ = 0.20, and 55 days until expiration. What is the premium on a knock-in call option with a down-and-in barrier of $48?
A) $0.175
B) $0.185
C) $0.195
D) $0.205
Q:
Assume S = $52, K = 50, div = 0.01, r = 0.06, σ = 0.22, and 45 days until expiration. What is the premium on an Asian average strike call where N = 1?
A) $0.00
B) $0.10
C) $0.20
D) $0.30
Q:
Assume S = $43, K = 45, div = 0.0, r = 0.09, σ = 0.36, and 90 days until expiration. What is the premium on an Asian average strike put where N = 3?
A) $0.26
B) $0.36
C) $0.46
D) $0.56
Q:
Assume S = $36, K = 35, div = 0.0, r = 0.08, σ = 0.40, and 270 days until expiration. What is the premium on an Asian average strike call where N = 2?
A) $1.91
B) $2.01
C) $2.11
D) $2.21
Q:
Assume S = $60, K = $60, r = 0.07, σ = 0.24, div = 0.02, and 90 days until expiration. What is the premium on an Asian average price put where N = 4?
A) $1.74
B) $1.84
C) $1.94
D) $2.04
Q:
Assume S = $55, K = $55, r = 0.07, σ = 0.27, div = 0.0, and 180 days until expiration. What is the premium on an Asian average price call, where N = 5?
A) $2.89
B) $2.99
C) $3.09
D) $3.19
Q:
The value of an Asian put option is computed using the geometric average strike. What is the expected payoff if the observed prices to date are 71, 72, 70, 68, 69, and 68, respectively?
A) 1.35
B) 1.45
C) 1.55
D) 1.65
Q:
The value of an Asian call option is computed using the geometric average strike. What is the expected payoff if the observed prices to date are 69, 70, 72, 71, 75, and 73, respectively?
A) 1.26
B) 1.36
C) 1.46
D) 1.56
Q:
What is the payoff on a 90 strike Asian option given it is a geometric average price put? The recent prices are 89, 90, 91, 87, 87, and 88.
A) 1.25
B) 1.35
C) 1.45
D) 1.55
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 net dollar gain or cost required to create a short put delta hedge against a 100 short put position? Assume puts are priced at $1.98, the delta is 0.489, the stock price is $34.50, and no cost to short stock.
A) $1,540.50 gain
B) $1,540.50 cost
C) $2,319.58 gain
D) $2,319.58 cost
Q:
Assume S = $33.00, σ = 0.32, r = 0.06, div = 0.01. You short 100 $35 strike puts at 68 days until expiration. Under a delta hedge position, what is your overnight profit/loss if the stock rises to $34.50? Assume no cost to short stock.
A) $8.30 gain
B) $8.30 loss
C) $9.56 gain
D) $9.56 loss
Q:
Assume that a $50 strike put pays a 2.0% continuous dividend, r = 0.07, σ = 0.25, and the stock price is $48.00. What is the profit or loss, per share, for a short put position if the option expires in 60 days and the price rises to $50.00 after 5 days?
A) $1.05 loss
B) $1.05 gain
C) $1.12 gain
D) $1.12 loss
Q:
Assume S = $33.00, σ = 0.32, r = 0.06, div = 0.01. You short 100 $35 strike calls at 68 days until expiration. Under a delta hedge position, what is your overnight profit/loss if the stock rises to $34.50?
A) $9.23 loss
B) $9.23 gain
C) $7.62 loss
D) $7.62 gain
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:
Assume that a $60 strike call pays a 1.0% continuous dividend, r = 0.05, σ = 0.28, and the stock price is $62.00. What is the profit or loss per share if on a long call position, with 73 days until expiration, the price immediately rises to $63.00?
A) $0.68 gain
B) $0.68 loss
C) $0.88 gain
D) $0.88 loss
Q:
Assume that a $50 strike call pays a 2.0% continuous dividend, r = 0.07, σ = 0.25, and the stock price is $48.00. What is the profit or loss, per share, for a short call position if the option expires in 60 days and the price rises to $50.00 after 5 days?
A) $0.84 gain
B) $0.84 loss
C) $0.95 gain
D) $0.95 loss
Q:
Discuss the three methods used to reduce the risk of extreme price moves. Ask the class to also elaborate on why simple delta hedging is inadequate to the task.
Q:
What are the two methods by which insurance companies hedge their risk of extreme losses?
Q:
What actions are required to both delta-hedge and gamma-hedge a written option position?
Q:
What prevents a market-maker from readjusting her delta hedge on a continual basis?
Q:
The equation used by Black and Scholes to characterize the behavior of an option, expressed with Greeks, holds true for American options as well as European options with one exception. What is the exception?
Q:
Describe the true relationship between option prices and delta. Use calls as an example.
Q:
Assume S = $62.50, σ = 0.20, r = 0.03, div = 0.0, on a $60 strike call and 81 days until expiration. Given a delta = 0.7092, gamma = 0.0582, and theta = -0.0158, what is the PREDICTED call price, using the delta, gamma, theta approach, after 1 day, assuming a $0.50 rise in the stock price?A) $4.364B) $4.376C) $4.390D) $4.392
Q:
Which of the following is NOT a source of cash while maintaining a delta neutral hedge?
A) Borrowing
B) Purchase or sale of shares
C) Interest
D) Self financing
Q:
Since delta of an option changes over the same time period that a stock price is changing, what is the delta used to calculate the approximate change in the option price?
A) Delta at the start of the time period
B) Delta at the end of the time period
C) The average delta over the time period
D) The median delta over the time period
Q:
Assume S = $56.00, σ = 0.45, r = 0.05, div = 0.0, on a $55 strike call and 45 days until expiration. Given delta = 0.6253, gamma = 0.0735, and theta = -0.0253, what is the approximate change in call price over 1 day, all else being the same?
A) $0.00
B) $0.01
C) $0.02
D) $0.03
Q:
Assume S = $45, σ = 0.25, r = 0.05, div = 0.0, on a 45 strike call and 55 days until expiration. Given delta = 0.5502 and gamma = 0.0876, what is the delta-gamma approximation for the call price on a $0.90 stock price decline?
A) $1.35
B) $1.45
C) $1.55
D) $1.65
Q:
Why do we care about Greeks?
Q:
What unique feature about perpetual options makes it possible to derive a valuation formula?
Q:
What is the difference between implied volatility and historical volatility?
Q:
What is the difference between a standard bull spread and a calendar bull spread?
Q:
Draw a payoff diagram for a long put position, depicting options that expire at 0, 30 and 60 days.
Q:
Which Greek is also called time decay and why?
Q:
As the date of expiration approaches, what change in theta might counteract or slow down the drop in the option price?A) DecreaseB) IncreaseC) Stay constantD) Indifferent
Q:
If an investor is speculating with a long call position, what is the most likely preference of the investor, relative to a change in rho?
A) Decrease
B) Increase
C) Stay constant
D) Indifferent
Q:
Assume that an investor is currently holding a reverse straddle position (i.e. a short put and short call), which is currently a profitable investment. All else being equal, what would this investor like to happen to vega?
A) Decrease
B) Increase
C) Stay constant
D) Indifferent
Q:
Suppose a $60 strike call has 45 days until expiration and pays a 1.5% continuous dividend. Assume S = $58.50, σ = 0.25, and r = 0.06. What is the option elasticity given an immediate price increase of $1.50?
A) 24.61
B) 18.61
C) 14.61
D) 9.61
Q:
Assume that a $75 strike call has a 1.0% continuous dividend, 90 days until expiration and stock price of $72.00. What is the rho of the option as the interest rate changes from 6.0% to 5.0%?
A) 0.07
B) 0.12
C) 0.16
D) 0.20
Q:
Assume that a $60 strike call has a 2.0% continuous dividend, r = 0.05, and the stock price is $61.00. What is the theta of the option as the expiration time declines from 60 to 50 days?
A) -0.52
B) -0.42
C) -0.32
D) -0.22
Q:
Suppose the 120-day futures price on crude oil is $115.00 per barrel and the volatility is 20.0%. Assume interest rates are 3.5%. What is the price of a $110 strike call futures option that expires in 120 days?
A) $3.09
B) $2.99
C) $2.89
D) $2.79
Q:
Suppose the 180-day futures price on crude oil is $110.00 per barrel and the volatility is 20.0%. Assume interest rates are 3.5%. What is the price of a $120 strike call futures option that expires in 180 days?
A) $1.89
B) $2.19
C) $2.59
D) $3.09
Q:
Suppose the spot exchange rate is $1.22 per British pound and the strike on a dollar denominated pound put is $1.20. Assume r = 0.04, rf = 0.05, σ = 0.20 and the option expires in 270 days. What is the put option price?
A) $0.075
B) $0.085
C) $0.095
D) $0.105
Q:
Suppose the spot exchange rate is $1.43 per British pound and the strike on a dollar denominated pound call is $1.30. Assume r = 0.045, rf = 0.06, σ = 0.15 and the option expires in 180 days. What is the call option price?
A) $0.133
B) $0.143
C) $0.153
D) $0.163
Q:
Assume that a $55 strike call has a 1.5% continuous dividend, r = 0.05 and the stock price is $50.00. If the option has 45 days until expiration, what is the vega, given a shift in volatility from 33.0% to 34.0%?
A) 0.20
B) 0.15
C) 0.10
D) 0.05
Q:
Assume that a $50 strike call has a 3.0% continuous dividend, σ = 0.27, r = 0.06 and 60 days from expiration. What is the gamma for a stock price movement from $48.00 to $49.00?
A) 0.046
B) 0.074
C) 0.089
D) 0.099