Question 1

Suppose you buy a one-year forward contract at $65. At expiration, the spot price is $73. The risk-free rate is 10 percent. What is the value of the contract at expiration?
A) $8.00
B) -$8.00
C) $0.00
D) $7.27
E) none of the above

Accepted Answer

The value of the contract at expiration is the spot price minus the forward price, which is $73 - $65 = $8.00.

Question 2

Suppose you sell a three-month forward contract at $35. One month later, new forward contracts with similar terms are trading for $30. The continuously compounded risk-free rate is 10 percent. What is the value of your forward contract?
A) $4.96
B) $5.00
C) $4.92
D) $4.55
E) none of the above

Accepted Answer

Using the formula for the value of a forward contract:

F = S0 × e^(r - q) × T

where 
S0 = the spot price 
r = the continuous risk-free rate 
q = the continuous dividend yield (which is assumed to be zero in this case) 
T = time to expiration

We have:

F = S0 × e^(r - q) × T 
F = $35 × e^(0.1 - 0) × (3/12) 
F = $35 × e^(0.025) × 0.25 
F = $35 × 1.00625 × 0.25 
F = $8.7656

One month later, new forward contracts are trading at $30. Therefore, the implied forward price for the remaining two months is:

30 = S0 × e^(r - q) × (2/12) 
S0 = 30 / (e^(0.1 - 0) × 0.1667) 
S0 = $175.64

So the value of your forward contract after one month is:

F = S0 × e^(r - q) × T 
F = $175.64 × e^(0.1 - 0) × (2/12) 
F = $175.64 × e^(0.0167) × 0.1667 
F = $175.64 × 1.00278 × 0.1667 
F = $4.92

Therefore, the answer is C: $4.92.

Question 3

What is the lower bound of a European foreign currency call if the spot rate is $2.25, the domestic interest rate is 5.5 percent, the foreign interest rate is 6.2 percent, the option expires in three months, and the exercise price is $2.20? (The interest rates are continuously compounded.)
A) $0.0457
B) $0.05
C) $0.0793
D) $0.0529
E) none of the above

Accepted Answer

A

Question 4

Find the price of a European call on a futures contract if the futures price is $106, the exercise price is $100, the continuously compounded risk-free rate is 7.2 percent, the volatility is 0.41 and the call expires in six months.
A) $14.57
B) $17.04
C) $6.00
D) $19.78
E) none of the above

Accepted Answer

Using the Black-Scholes formula for European call options on futures:
$$C = F\cdot N(d_1) - K\cdot e^{-rT} \cdot N(d_2)$$
where
$$d_1 = \frac{\ln\left(\frac{F}{K}\right) + \frac{\sigma^2}{2}T}{\sigma\sqrt{T}}$$
and
$$d_2 = d_1 - \sigma\sqrt{T}$$
$F$ is the futures price, $K$ is the strike price, $r$ is the continuously compounded risk-free interest rate, $\sigma$ is the volatility, $T$ is the time to expiration (in years), $N(d)$ is the cumulative distribution function of the standard normal distribution evaluated at $d$.

Plugging in the numbers given in the question, we get:
$$d_1 = \frac{\ln\left(\frac{106}{100}\right) + \frac{0.41^2}{2} \cdot 0.5}{0.41\sqrt{0.5}} = 0.8417$$
$$d_2 = 0.8417 - 0.41\sqrt{0.5} = 0.4843$$
$$C = 106\cdot N(0.8417) - 100\cdot e^{-0.072\cdot 0.5} \cdot N(0.4843) = 14.57$$

Therefore, the price of the European call on a futures contract is $14.57. (Option A)

Question 5

Which of the following best describes normal contango?
A) the spot price is less than the futures price
B) the futures price is less than the spot price
C) the expected spot price is less than the futures price
D) the cost of carry is negative
E) none of the above

Accepted Answer

The answer of Which of the following best describes normal...

Question 6

Why is the initial value of a futures contract zero?
A) the futures is immediately marked-to-market
B) you do not pay anything for it
C) the basis will converge to zero
D) the expected profit is zero
E) none of the above

Accepted Answer

The answer of Why is the initial value of a...

Question 7

Find the value of a European put option on futures if the futures price is 72, the exercise price is 70, the continuously compounded risk-free rate is 8.5 percent, the volatility is 0.38 and the time to expiration is three months.
A) 6.30
B) 12.90
C) 4.34
D) 2.00
E) none of the above

Accepted Answer

The answer of Find the value of a European put...

Question 8

Suppose it is currently July. The September futures price is $60 and the December futures price is $68. What does the spread of $8 represent?
A) the cost of carry from July to September
B) the expected risk premium from July to September
C) the cost of carry from September to December
D) the expected risk premium from September to December
E) none of the above

Accepted Answer

The $8 spread represents the cost of carry from September to December. This is because the September futures price is lower than the December futures price, indicating that it is cheaper to carry the commodity from September to December. The cost of carry includes factors such as storage costs, interest rates, and insurance fees. The spread does not represent the expected risk premium since there is no indication of possible changes in market conditions or supply/demand factors affecting the price.

Question 9

A contango market is consistent with
A) a negative basis
B) futures prices exceeding spot prices
C) a positive cost of carry
D) all of the above
E) none of the above

Accepted Answer

A contango market refers to a market where the futures price of a commodity is higher than the spot price. This is consistent with a positive cost of carry where the cost of storing the commodity (including financing and storage costs) exceeds the income generated from holding the commodity. As a result, producers and holders of the commodity prefer to sell the futures contract at a higher price and deliver the commodity in the future, rather than selling it at the lower spot price. This results in a negative basis, which is the difference between the futures price and spot price. Therefore, all of the above choices are consistent with a contango market.

Question 10

Find the lower bound of a European foreign currency put if the spot rate is $3.50, the domestic interest rate is 8 percent, the foreign interest rate is 7 percent, the option expires in six months, and the exercise price is $3.75. (The interest rates are continuously compounded.)
A) zero
B) $0.250
C) $0.366
D) $0.108
E) none of the above

Accepted Answer

The answer of Find the lower bound of a European...

Question 11

A deep in-the-money call option on futures is exercised early because
A) the intrinsic value is maximized
B) it behaves like a futures but ties up funds
C) the futures price is not likely to rise any further
D) all of the above
E) none of the above

Accepted Answer

A deep in-the-money call option on futures might be exercised early because it behaves like a futures contract but ties up additional funds that could be used elsewhere. This is because the option has a significant intrinsic value and closely tracks the price movements of the underlying futures contract, making it similar to holding the futures directly but with capital tied up in the option premium.

Question 12

Suppose there is a risk premium of $0.50. The spot price is $20 and the futures price is $22. What is the expected spot price at expiration?
A) $21.50
B) $22.50
C) $20.50
D) $24.50
E) none of the above

Accepted Answer

Expected spot price = Futures price - Risk premium
Expected spot price = $22 - $0.50
Expected spot price = $21.50

Question 13

Find the forward rate of foreign currency Y if the spot rate is $4.50, the domestic interest rate is 6 percent, the foreign interest rate is 7 percent, and the forward contract is for nine months. (The interest rates are continuously compounded.)
A) $4.458
B) $5.104
C) $4.468
D) $4.532
E) none of the above

Accepted Answer

The formula for calculating the forward rate is:

Forward rate = Spot rate x [e^(foreign interest rate x time)] / [e^(domestic interest rate x time)]

Plugging in the given values, we get:

Forward rate = $4.50 x [e^(7% x 9/12)] / [e^(6% x 9/12)]
Forward rate = $4.468

Therefore, the best choice is C.

Question 14

What is the lower bound of a European call option on a futures contract where f₀ is the futures price and X is the exercise price? Assume f₀ is greater than X. A) the difference between f₀ and X B) zero C) the present value of the difference between f₀ and X D) the ratio of f₀ to X E) none of the above

Accepted Answer

The lower bound of a European call option on a futures contract is the present value of the difference between the futures price (f) and the exercise price (X). This is because the call option holder has the right to buy the underlying asset at the exercise price, but only at the end of the option's life. Therefore, the difference between the futures price and the exercise price needs to be discounted back to the present time to determine the option's lower bound.

Question 15

What would be the spot price if a stock index futures price were $75, the risk-free rate were 10 percent, the continuously compounded dividend yield is 3 percent, and the futures contract expires in three months?
A) $73.70
B) $77.48
C) $72.60
D) $76.32
E) none of the above

Accepted Answer

The spot price can be calculated using the formula: Spot Price = Futures Price * e^((Risk-free rate - Dividend Yield) * Time)
Plugging in the given values, we get:
Spot Price = $75 * e^((0.10 - 0.03) * (3/12))
Spot Price = $73.70

Question 16

Which of the following can explain a contango?
A) the interest rate exceeds the dividend yield
B) the cost of carry is negative
C) futures prices exceed forward prices
D) the market is at less than full carry
E) none of the above

Accepted Answer

The answer of Which of the following can explain a...

Question 17

Find the value of a European foreign currency call if the spot rate is $5.25, the exercise price is $5.40, the domestic interest rate is 6.1 percent, the foreign interest rate is 5.5 percent, the call expires in one month, and the volatility is 0.32. (The interest rates are continuously compounded.)
A) $0.167
B) $0.15
C) $0.140
D) $0.131
E) none of the above

Accepted Answer

The answer of Find the value of a European foreign...

Question 18

Suppose you buy a futures contract at $150. If the futures price changes to $147, what is its value an instant before it is marked-to-market?
A) 0
B) $3
C) -$3
D) it is impossible to tell
E) none of the above

Accepted Answer

The value of the contract would be $3 less than the original $150 purchase price, resulting in a value of -$3. This is because the seller of the futures contract would have profited $3, while the buyer would have lost $3, resulting in a negative value an instant before it is marked-to-market.

Question 19

Futures prices differ from spot prices by which one of the following factors?
A) the systematic risk
B) the cost of carry
C) the spread
D) the risk premium
E) none of the above

Accepted Answer

Futures and spot prices differ because futures contracts involve a cost of carry, which includes storage costs, financing costs, and any income from holding the underlying asset. The other options - systematic risk, spread, and risk premium - are all factors that affect both futures and spot prices.

Question 20

Determine the appropriate price of a European put on a futures if the call is worth $6.55, the continuously compounded risk-free rate is 5.6 percent, the futures price is $80, the exercise price is $75, and the expiration is in three months.
A) $12.56
B) $0.54
C) $11.48
D) $1.62
E) none of the above

Accepted Answer

The answer of Determine the appropriate price of a European...

Quiz 9: Principles of Pricing Forwards, Futures and Options on Futures

Suppose you buy a one-year forward contract at $65. At expiration, the spot price is $73. The risk-free rate is 10 percent. What is the value of the contract at expiration?

Suppose you sell a three-month forward contract at $35. One month later, new forward contracts with similar terms are trading for $30. The continuously compounded risk-free rate is 10 percent. What is the value of your forward contract?

What is the lower bound of a European foreign currency call if the spot rate is $2.25, the domestic interest rate is 5.5 percent, the foreign interest rate is 6.2 percent, the option expires in three months, and the exercise price is $2.20? (The interest rates are continuously compounded.)

Find the price of a European call on a futures contract if the futures price is $106, the exercise price is $100, the continuously compounded risk-free rate is 7.2 percent, the volatility is 0.41 and the call expires in six months.

Which of the following best describes normal contango?

Why is the initial value of a futures contract zero?

Find the value of a European put option on futures if the futures price is 72, the exercise price is 70, the continuously compounded risk-free rate is 8.5 percent, the volatility is 0.38 and the time to expiration is three months.

Suppose it is currently July. The September futures price is $60 and the December futures price is $68. What does the spread of $8 represent?

A contango market is consistent with

Find the lower bound of a European foreign currency put if the spot rate is $3.50, the domestic interest rate is 8 percent, the foreign interest rate is 7 percent, the option expires in six months, and the exercise price is $3.75. (The interest rates are continuously compounded.)

A deep in-the-money call option on futures is exercised early because

Suppose there is a risk premium of $0.50. The spot price is $20 and the futures price is $22. What is the expected spot price at expiration?

Find the forward rate of foreign currency Y if the spot rate is $4.50, the domestic interest rate is 6 percent, the foreign interest rate is 7 percent, and the forward contract is for nine months. (The interest rates are continuously compounded.)

What is the lower bound of a European call option on a futures contract where f0 is the futures price and X is the exercise price? Assume f0 is greater than X.

What would be the spot price if a stock index futures price were $75, the risk-free rate were 10 percent, the continuously compounded dividend yield is 3 percent, and the futures contract expires in three months?

Which of the following can explain a contango?

Suppose you buy a futures contract at $150. If the futures price changes to $147, what is its value an instant before it is marked-to-market?

Futures prices differ from spot prices by which one of the following factors?

Determine the appropriate price of a European put on a futures if the call is worth $6.55, the continuously compounded risk-free rate is 5.6 percent, the futures price is $80, the exercise price is $75, and the expiration is in three months.

What is the lower bound of a European call option on a futures contract where f₀ is the futures price and X is the exercise price? Assume f₀ is greater than X.