Deck 28: Pricing of Futures and Options Contracts

Question 1

You borrow $200 at 10% per year and proceed to buy Asset XYZ for $200 in the cash market. This asset pays $5 quarterly. You then immediately sell a futures contract at $214 requiring delivery of asset XYZ in three months. Which of the below statements is TRUE?

A) At the end of three month, the settlement of the futures contract generates a total proceeds of $220.
B) At the end of three month, the cost of the loan generates a total outlay of $206
C) Your strategy of selling the futures contract after borrowing money to buy the asset produces a net profit of $15.
D) None of these

Answer 1

D

Question 2

Consider the "reverse cash and carry trade" where you buy the futures contract, short sell Asset XYZ, and invest or lend at a rate of r until the settlement date. In computing the "profit," which of the below statements is TRUE?

A) Profit = Total proceeds + Total outlay
B) Profit = P - rP + (F - yP)
C) Profit = Total outlay Profit - Total proceeds
D) Profit = P + rP - (F + yP)

Answer 2

D

Question 3

According to arbitrage arguments, the equilibrium or theoretical futures price can be determined on the basis of ________.

A) the price of the asset in the options market.
B) the net book income on the asset until the settlement date.
C) the financing cost, which is the interest rate for borrowing and lending until the settlement date.
D) None of these

Answer 3

C

Question 4

Solving for the theoretical futures price, we get ________.

A) F = P + P(y - r).
B) F = P + P(r - y).
C) F = P - P(r + y).
D) P = F + F(r - y).

Question 5

Consider the "cash and carry trade" where you sell (or take a short position in) the futures contract, purchase Asset XYZ, and borrow until the settlement date. In computing the value "from the loan," which of the below statements is TRUE?

A) P = repayment of principal of loan
B) rP = interest on loan
C) P + rP = total outlay
D) All of these

Question 6

Consider the "cash and carry trade" where you sell (or take a short position in) the futures contract, purchase Asset XYZ, and borrow at a rate of r until the settlement date. In computing the value "from settlement of the futures contract," which of the below statements is FALSE?

A) F = proceeds from sale of Asset XYZ to settle the futures contract
B) yP = payment received from investing in Asset XYZ
C) F - yP = total proceeds
D) All of these

Question 7

You borrow $5,000 at 8% per year and proceed to buy Asset XYZ for $5,000 in the cash market. This asset pays $100 quarterly. You then immediately sell a futures contract at $5,500 requiring delivery of asset XYZ in three months. Which of the below statements is TRUE?

A) At the end of three month, the settlement of the futures contract generates a total proceeds of $5,600.
B) At the end of three month, the cost of the loan generates a total outlay of $5,100
C) Your strategy of selling the futures contract after borrowing money to buy the asset produces a net profit of $500.
D) All of these

Question 8

When developing a theory of futures pricing, which of the following is NOT a notation that is used?

A) F = Futures price ($)
B) C = Cash market price ($)
C) r = Financing cost (%)
D) y = Cash yield (%)

Question 9

Which of the below statements is FALSE?

A) For strategies applied to stock index futures, a short sale of the stocks in the index means that all stocks in the index must be sold at different times.
B) When illustrating arbitrage strategies, one assumes that (1) only one asset is deliverable, and (2) the settlement date occurs at a known, fixed point in the future.
C) Some futures contracts involve a single asset, but other contracts apply to a basket of assets or an index.
D) The basic arbitrage model presented in this chapter ignores not only taxes but also different tax treatment of cash market transactions and futures transactions.

Question 10

Consider the "cash and carry trade" where you sell (or take a short position in) the futures contract, purchase Asset XYZ, and borrow until the settlement date. In computing the "profit," which of the below statements is TRUE?

A) Profit = Total proceeds - Total outlay
B) Profit = F + yP + (P - rP)
C) Profit = Total outlay - Total proceeds
D) Profit = P + yP - (P + rF)

Question 11

You lend $2,000 at 12% per year for three months and proceed to short sell Asset XYZ for $2,000 in the cash market. You are required to pay $200 to the lender of Asset XYZ (which is the proceeds the lender would have received). You then immediately buy a futures contract at $1,850 for delivery of asset XYZ in three months (this will cover your short position). What is the net profit or loss from your strategy of lending money, short selling, and buying the futures contract?

A) $30
B) $20
C) $10
D) $0

Question 12

Consider the "reverse cash and carry trade" where you buy the futures contract, short sell Asset XYZ, and invest or lend until the settlement date. In computing the value "from the loan," which of the below statements is TRUE?

A) rP= principal from maturing of investment
B) P = interest earned on loan
C) P + rP = total proceeds
D) P - rP = payment received from investing in Asset XYZ

Question 13

Which of the below statements is FALSE?

A) The theoretical futures price may be at a premium to the cash market price (higher than the cash market price) or at a discount from the cash market price (lower than the cash market price), depending on the value of P(r - y).
B) The term, r - y, which reflects the difference between the cost of financing and the asset's cash yield, is called the net financing cost.
C) The net financing cost is more commonly called the cost of carry, or simply, carry.
D) Negative carry means that the yield earned is greater than the financing cost; positive carry means that the financing cost exceeds the yield earned.

Question 14

You lend $200 at 8% per year for three months and proceed to short sell Asset XYZ for $200 in the cash market. You are required to pay $6 to the lender of Asset XYZ (which is the proceeds the lender would have received). You then immediately buy a futures contract at $184 for delivery of asset XYZ in three months (this will cover your short position). What is the net profit or loss from your strategy of lending money, short selling, and buying the futures contract?

A) $14
B) $10
C) -$7
D) -$14

Question 15

You borrow $1,000 at 16% per year and proceed to buy Asset XYZ for $1,000 in the cash market. This asset pays $10 quarterly. You then immediately sell a futures contract at $1,025 requiring delivery of asset XYZ in three months. What is the net profit or loss from your strategy of selling the futures contract after borrowing money to buy the asset ?

A) $50.
B) $10.
C) -$5.
D) -$10.

Question 16

In summarizing the effect of carry on the difference between the futures price and the cash market price in this way, which of the below statements is FALSE?

A) If the carry is positive (y > r), then the futures price will sell at a discount to cash price (F < P).
B) If the carry is negative (r > y), then the futures price will sell at a premium to cash price (F > P).
C) If the carry is zero (r = y), then the futures price will be equal to the cash price (F = P).
D) None of these

Question 17

Which of the below statements is FALSE?

A) It is important to note that, in the absence of initial and variation margins, the theoretical price for the contract is technically the theoretical price for a forward contract, not the theoretical price for a futures contract.
B) For cash and carry trade, the futures price that would produce no arbitrage profit is: F = P + P(rB - y) where P is the repayment of principal of loan, rB is the borrowing rate, and y is the cash yield.
C) For reverse cash and carry trade, the futures price that would prevent a riskless profit is: F = P + P(rL - y) where P is the repayment of principal of loan, rL is the lending rate, and y is the cash yield.
D) In deriving the theoretical futures price, we consider transaction costs of the elements in the arbitrage strategies.

Question 18

Which of the below statements is FALSE?

A) A cash and carry trade strategy includes selling a futures contract and borrowing cash to purchase a security that is "carried" to the futures settlement date.
B) A reverse cash and carry trade strategy includes buying a futures contract, short selling a security and lending the proceeds.
C) There exists a futures price that would prevent the opportunity for the riskless arbitrage profit.
D) An equilibrium futures price is a futures price where any higher or lower futures price would disallow riskless arbitrage profits.

Question 19

Consider the "reverse cash and carry trade" where you buy the futures contract, short sell Asset XYZ, and invest or lend at a rate of r until the settlement date. In computing the value "from settlement of the futures contract," which of the below statements is TRUE?

A) F = proceeds from sale of Asset XYZ to settle the futures contract
B) yP = payment received from investing in Asset XYZ
C) F + yP = total proceeds
D) None of these

Question 20

You lend $1,000 at 10% per year for three months and proceed to short sell Asset XYZ for $1,000 in the cash market. You are required to pay $75 to the lender of Asset XYZ (which is the proceeds the lender would have received). You then immediately buy a futures contract at $950 for delivery of asset XYZ in three months (this will cover your short position). What is the net profit or loss from your strategy of lending money, short selling, and buying the futures contract?

A) $50
B) $25
C) $0
D) -$25

Question 21

To show how to calculate the hedge ratio, we use notation that includes the following: ________.

A) S = current asset price and C = current price of a call option.
B) Cd = intrinsic value of the call option if the asset price goes up and E = strike price of the call option.
C) d = current price of a call option and r = a risk-free one-period interest rate .
D) E = strike price of the call option and u = current asset price.

Question 22

For ________ options, as the time remaining until expiration decreases, the option price approaches its intrinsic value.

A) intrinsic Asian
B) extrinsic Asian
C) American
D) European

Question 23

The option price will change as the price of the ________. For a ________, as the price of the underlying asset increases (all other factors constant), the option price increases. The opposite holds for a ________.

A) underlying asset changes; put option; call option
B) underlying asset changes; call option; put option
C) European option changes; call option; put option
D) American option changes; put option; call option

Question 24

Factors influence the price of an option include the ________.

A) future price of the underlying asset and the strike price.
B) time to expiration of the option and the expected price volatility of the underlying asset over the past year.
C) long-term and the risk-free interest rate over the life of the option.
D) the strike price and the anticipated cash payments on the underlying asset over the life of the option.

Question 25

It can be shown that the put-call parity relationship for options where the underlying asset makes cash distributions and where the time value of money is recognized is: Put option price - Call option price = ________.

A) Present value of strike price - Present value of cash distribution + Price of underlying asset
B) Present value of strike price + Future value of cash distribution - Price of underlying asset
C) Present value of strike price + Present value of cash distribution - Price of underlying asset
D) Future value of strike price + Present value of cash distribution - Price of underlying asset

Question 26

If the strike price for a call option is $10 and the current asset price is $9, the intrinsic value is ________.

A) $10.
B) $9.
C) $1.
D) zero

Question 27

The ________ is fixed for the life of the option. All other factors equal, the lower the strike price, the ________ the price for a call option. For put options, the ________ the exercise price, the higher the option price.

A) strike price; lower; higher
B) exercise price; higher; lower
C) strike price; higher; higher
D) market price; lower; lower

Question 28

An option buyer can realize the value of a position taken in the option by ________.

A) exercising the option.
B) selling the option for its exercise price.
C) buying a put option.
D) selling a put option.

Question 29

Because of the assumptions required for the binomial model described above, such models may have limited applicability to the pricing of options on ________.

A) call options
B) hedge ratios
C) dividend paying securities.
D) fixed-income securities.

Question 30

If the strike or exercise price for a put option is $75, and the current asset price is $75, and the market value of the put option is $77. What is the time premium of the put option?

A) $7
B) $2
C) $1
D) zero

Question 31

To determine the value of the ________, H, we must know Cᵤ and Cd. These two values are equal to the difference between the price of the asset and the strike price in the two possible states.

A) put option
B) call option
C) hedge ratio
D) payoff ratio

Question 32

To derive a one-period binomial option pricing model for a call option, we begin by constructing a portfolio consisting of ________.

A) a short position in a certain amount of the asset, and a short call position in the underlying asset.
B) a long position in a certain amount of the asset, and a long call position in the underlying asset.
C) a short position in a certain amount of the asset, and a long call position in the underlying asset.
D) a long position in a certain amount of the asset, and a short call position in the underlying asset.

Question 33

All other factors equal, the ________ the expected volatility (as measured by ________) of the price of the underlying asset, the more an investor would be willing to pay for the option, and the more an option writer would demand for it.

A) lower; the variance
B) lower; the standard deviation
C) greater; beta
D) greater; the standard deviation

Question 34

Suppose a portfolio consisting of the long position in the asset and the short position in the call option is riskless and will produce a return that equals the risk-free interest rate. A portfolio constructed in this way is called ________.

A) a risk-reduced portfolio.
B) an unhedged portfolio.
C) a hedged portfolio.
D) a speculative portfolio.

Question 35

________ on the underlying asset tend to decrease the price of a call option because the cash payments make it more attractive to hold the underlying asset than to hold the option. For put options, ________ on the underlying asset tend to increase the price.

A) Noncash payments; cash payments
B) Cash payments; noncash payments
C) Cash payments; cash payments
D) Noncash payments; noncash payments

Question 36

________ is an important relationship between the price of a call option and the price of a put option on the same underlying instrument, with the same strike price and the same expiration date.

A) The call-put premium relationship
B) The put-call parity relationship
C) The put-call discount relationship
D) The call-put relationship

Question 37

To derive the price of a ________, we can rely on the basic principle that the hedged portfolio, being riskless, must have a return equal to the risk-free rate of interest.

A) hedge ratio
B) put option
C) call option
D) futures price

Question 38

All other factors constant, the higher the short-term, risk-free interest rate, the ________ the cost of buying the underlying asset and carrying it to the ________ of the call option.

A) greater; expiration date
B) lower; maturity date
C) greater; ex-dividend date
D) lower; salvage date

Question 39

The ________ is the sum of the option's intrinsic value and a premium over intrinsic value that is often referred to as the ________.

A) option price time value or time premium.
B) forward value time value or time discount.
C) futures value time value or time premium.
D) option price time value or time discount.

Question 40

The ________ of an option, at any time, is its economic value if it is exercised immediately. If no positive economic value would result from exercising immediately, ________.

A) extrinsic value; extrinsic value is zero.
B) intrinsic value; intrinsic value is zero.
C) extrinsic value; intrinsic value is negative.
D) intrinsic value; intrinsic value is positive.

Question 41

The theoretical futures price depends on the price of the underlying asset in the futures market, the cost of financing a position in the underlying asset, and the cash yield on the underlying asset.

Question 42

What is the time premium of an option?

Question 43

Describe an option when (i) in the money and (ii) out of the money.

Question 44

The equilibrium or theoretical futures price can be determined through arbitrage arguments.

Question 45

The actual futures price will diverge from the theoretical futures price because of interim cash flows, differences between lending and borrowing rates, transaction costs, restrictions on short selling, and uncertainty about the deliverable asset and the date it will be delivered.

Question 46

To determine the value of the hedge ratio, H, what two values must we know? What are these values equal to?

Question 47

The price of an option can be separated into two parts, its extrinsic value and its risk premium.

Question 48

What do we assume when we illustrate arbitrage strategies?

Question 49

The put-call parity relationship is the relationship between the price of a call option and the price of a put option on the same underlying instrument, with the same strike price and the same expiration date.

Question 50

According to the arbitrage arguments, what information determines the equilibrium or theoretical futures price?

Question 51

The strength of the binomial model based on yields is that it satisfies the put-call parity relationship by taking into consideration the yield curve, thereby allowing arbitrage opportunities.

Question 52

There are six factors that influence the price of an option. Describe four of these factors. What may these factors depend on?

Question 53

The value of an option is greater than the cost of creating a replicating hedge portfolio.

Question 54

The strategy that can be used to capture the arbitrage profit for an overpriced futures contract is the reverse cash and carry trade; the strategy that can be used to capture the arbitrage profit for an underpriced futures contract is the cash and carry trade.

Question 55

At the delivery date, the price of a futures contract diverges from the cash market price.

Question 56

There are six factors that influence the price of an option: the current price of the underlying asset, the strike price, the time to expiration of the option, the expected price volatility of the underlying asset over the life of the option, the short-term, risk-free interest rate over the life of the option, and the anticipated cash payments on the underlying asset over the life of the option.

Question 57

Several models have been developed to determine the theoretical value of an option.

Question 58

The theoretical price of a futures contract can be determined on the basis of arbitrage arguments, but is much more complicated to determine than the theoretical price of an option because the option price depends on the expected price volatility of the underlying asset over the life of the option.