Question 1

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 prices are determined by the cost of carrying the underlying asset until the futures contract expiration date. In contrast, spot prices are the current market price for the underlying asset. Therefore, the difference between futures prices and spot prices is primarily determined by the cost of carry, which includes factors such as storage costs, financing costs, and insurance costs. Choices A, C, and D are not direct factors in determining the difference between futures prices and spot prices. Therefore, the correct answer is B.

Question 2

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 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

The lower bound of a European call option is calculated using the formula: C ≥ S * e^(-r_f * T) - X * e^(-r_d * T). Substituting the given values: C ≥ 2.25 * e^(-0.062 * 0.25) - 2.20 * e^(-0.055 * 0.25) = 0.0457.

Question 4

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

Using the put-call parity for futures options: P = C + Xe^(-rT) - F. Substituting the given values, P = 6.55 + 75e^(-0.056*0.25) - 80 = 1.62.

Question 5

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 6

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 7

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

In a contango market, futures prices exceed spot prices, which is consistent with a positive cost of carry. As a result, the basis (difference between futures and spot prices) is negative. So all of the above options are correct.

Question 8

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

Using the formula:

Forward rate = spot rate × e^((foreign interest rate - domestic interest rate) × time)

Forward rate = 4.5 × e^((0.07 - 0.06) × 0.75)

Forward rate = 4.5 × e^(0.0075)

Forward rate = 4.468

Therefore, the forward rate of foreign currency Y is $4.468. The closest option to this is option C, so the answer is C.

Question 9

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 10

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 11

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

Normal contango occurs when the expected future spot price is less than the futures price, reflecting the cost of carry and risk premium.

Question 12

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 spread of $8 represents the difference between the September futures price and the December futures price. Since the December price is higher than the September price, this indicates that there is a cost of carry from September to December, which is represented by the $8 spread. The cost of carry includes things like storage costs, financing costs, and insurance costs associated with holding the underlying asset. The spread does not represent a risk premium, as there is no indication of increased risk associated with either futures contract.

Question 13

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 14

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 futures contract is based on the difference between the entry price and the current price. In this case, the price has decreased by $3, so the value of the contract has decreased by $3 as well, resulting in a value of -$3.

Question 15

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 value of a European put option on futures can be calculated using the Black-Scholes formula for options on futures. Given the inputs, the calculated value of the put option is approximately 4.34.

Question 16

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

First, we need to calculate the present value of the forward contract using the continuously compounded risk-free rate:

PV = 35e^(-0.1*3/12) = 33.98

After one month, the new forward contracts are trading for $30, but we already sold our contract for $35, so we have gained a profit of $5. However, we need to discount this profit back to the present value using the continuously compounded risk-free rate:

Profit = $5e^(-0.1*2/12) = $4.92

Therefore, the value of our forward contract is:

Value = PV + Profit = $33.98 + $4.92 = $38.90

But since we sold the contract for $35, our net gain is:

Net Gain = Value - Sale Price = $38.90 - $35 = $3.90

Therefore, the correct answer is C) $4.92, which is the present value of our anticipated profit.

Question 17

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 18

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 19

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

Contango occurs when the futures price is higher than the expected future spot price, often due to the cost of carry, which includes storage costs and interest rates. If the interest rate exceeds the dividend yield, it contributes to a positive cost of carry, leading to contango.

Question 20

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.

Quiz 8: Principles of Pricing Forwards,futures and Options on Futures

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

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.

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. )

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.

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. )

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 contango market is consistent with

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. )

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. )

Why is the initial value of a futures contract zero?

Which of the following best describes normal contango?

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?

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?

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?

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 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 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?

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

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.