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

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

Answer 1

A

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

Answer 2

C

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

Answer 3

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Question 21

Value is created in a futures contract with the passage of time.

Question 22

Under uncertainty and risk aversion, today's spot price equals

A) the expected future spot price, minus the storage costs, minus the interest forgone, minus the risk premium
B) the expected future spot price, minus the storage costs, minus the interest forgone, plus the risk premium
C) the expected future spot price, minus the storage costs, minus the risk premium
D) the future spot price minus the cost of storage
E) none of the above

Question 23

A synthetic put option on futures could be constructed by buying a call option on futures and selling the futures.

Question 24

A convenience yield is an explanation for a negative cost of carry.

Question 25

The cost of carry consists of all the following except

A) the risk-free rate
B) the cost of storage
C) insurance on the asset
D) the risk premium
E) none of the above

Question 26

A transaction that exploits differences in the theoretical and actual values of a foreign currency forward or futures contract is called

A) covered interest arbitrage
B) triangular arbitrage
C) a conversion
D) interest-rate parity
E) none of the above

Question 27

The value of a futures contract immediately after being marked to market is

A) numerically equal to the daily settlement amount
B) the spot price plus the original forward price
C) equal to the amount by which the price changed since the contract was opened
D) simply zero
E) none of the above

Question 28

A normal market in which the futures price exceeds the spot price is described as a contango.

Question 29

The additional return earned by holding a commodity that is in short supply or a nonpecuniary gain from an asset is referred to as

A) the negative cost of carry
B) the convenience yield
C) cash-flow free gains
D) gains on the underlying
E) none of the above

Question 30

Determine the value of a European foreign currency put if the call is at $0.05, the spot rate is $0.5702, the exercise price is $0.59, the domestic interest rate is 5.75 percent, the foreign interest rate is 4.95 percent and the options expire in 45 days. (The interest rates are continuously compounded.)

A) $0.069
B) $0.031
C) $0.050
D) $0.517
E) none of the above

Question 31

The futures price of a non-storable asset is determined by the cost of carry.

Question 32

The Black formula prices an option on an instrument with a positive cost of carry.

Question 33

The spot price plus the cost of carry equals

A) the convenience yield
B) the expected future spot price
C) the risk premium
D) the futures price
E) none of the above

Question 34

The daily settlement brings the value of a futures contract back to zero.

Question 35

The dividends that are subtracted from the cost of storage to determine the cost of carry are actually the present value of future dividends.

Question 36

Interest rate parity is essentially the same as

A) the cross-rate relationship
B) the cost of carry relationship
C) the Garman-Kohlhagen model
D) all of the above
E) none of the above

Question 37

The risk-free rate is missing from d₁ in the Black model because it is effectively zero.

Question 38

Put-call-futures parity is the relationship between the prices of puts, calls, and futures on an asset. Assuming a constant risk-free rate and European options, which of the following correctly expresses the relationship of put-call-futures parity?

A) Pe(S0,T) = Ce(S0,T) + (X - f0(T))(1 + r)-T
B) Pe(S0,T,X) = Ce(S0,T) - (X - f0(T))(1 + r)-T
C) Pe(S0,T,X) = Ce(S0,T,X) + (X - f0(T))(1 + r)-T
D) Pe(S0,T,X) = Ce(S0,T,X)(X - f0(T))(1 + r)-T
E) none of the above

Question 39

The cost of carry futures pricing model requires that investors be able to sell short the commodity.

Question 40

The value of a long position in a forward contract at expiration is

A) the spot price plus the original forward price
B) the spot price minus the original forward price
C) the original forward price discounted to expiration
D) the spot price minus the original forward price discounted to expiration
E) none of the above

Question 41

The cost of carry includes the interest lost on the funds tied up in the asset stored.

Question 42

As soon as a futures contract is marked to market, its value is zero.

Question 43

American foreign currency calls will never be exercised early.

Question 44

Under uncertainty and risk neutrality, today's spot price equals the expected future spot price minus the cost of storage and interest forgone.

Question 45

The price of a futures spread reflects the cost of carry until the time the spread is closed.

Question 46

The Black-Scholes-Merton formula can be used in place of the Black formula if you use the futures price for the stock price and a risk-free rate of zero.

Question 47

Forward and futures prices will be equal prior to expiration if interest rates are certain or if futures prices and interest rates are correlated.

Question 48

The price of a futures contract that expires immediately is the spot price.

Question 49

Interest-rate parity is a cost-of-carry model.

Question 50

Holding everything else constant, dividends or interest on the underlying commodity would make a futures price be higher.

Question 51

If the exercise price equals the futures price, a put on the futures will have the same price as a call on the futures.

Question 52

If the U.S. government announced that it would allow the dollar to drop in foreign currency markets, the price of a euro put would probably fall.

Question 53

If the U.S. risk-free rate is 4 percent and the Swiss risk-free rate is 5 percent, a U.S. investor can earn the Swiss rate by buying Swiss francs, selling a forward or futures contract and converting back to dollars at the contract's expiration.

Question 54

A market in which the futures price is said to be unbiased is also a market in which there is a risk premium.

Question 55

A stock index futures price is the stock price compounded to expiration at the risk-free rate plus the future value of the dividends.

Question 56

If one buys an asset, sells a futures, and holds the position until expiration, it is equivalent to selling the asset at the original futures price.

Question 57

In financial futures markets, contango means that long-term interest rates are less than short-term interest rates.

Question 58

A futures contract can have negative value.

Question 59

The dividend yield on a stock option is similar to the foreign interest rate on a foreign currency option.

Question 60

Normal backwardation and contango are mutually exclusive conditions for a market.