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

Question 1

What is the lower bound of a European call on a futures 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

Answer 1

C

Question 2

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

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?

A)$0.0457
B)$0.05
C)$0.0793
D)$0.0529
E)none of the above

Answer 3

A

Question 4

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 .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 5

Find the price of a European call on a futures if the futures price is $106,the exercise price is $100,the continuously compounded risk-free rate is 7.2 percent,the volatility is .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 6

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 7

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 8

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 9

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 10

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 11

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

A)$73.70
B)$77.48
C)$72.60
D)$76.32
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 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 .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 14

Determine the appropriate price of a European put on a futures if the call is worth $6.55,the 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 15

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 16

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

Question 17

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.

A)zero
B)$0.250
C)$0.366
D)$0.108
E)none of the above

Question 18

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 19

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

A)$4.96
B)$5.00
C)$4.92
D)$4.55
E)none of the above

Question 20

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.

A)$4.458
B)$5.104
C)$4.468
D)$4.532
E)none of the above

Question 21

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 22

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 23

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

Question 24

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

Question 25

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

Question 26

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 27

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 28

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

Question 29

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

Question 30

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

Question 31

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

Question 32

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

Question 33

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 34

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 35

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 36

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

Question 37

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

Question 38

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.

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

Question 39

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

Question 40

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

Question 41

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

Question 42

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

Question 43

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 44

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 45

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

Question 46

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

Question 47

American foreign currency calls will never be exercised early.

Question 48

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

Question 49

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 50

A futures contract can have negative value.