Derivatives

Question 1

How does future contracts and forward contracts relate?

Answer 1

• futures contract is a standardized forward contract, a legal agreement to buy or sell something at a predetermined price at a specified time in the future, between parties not known to each other.
• Futures are traded on an exchange whereas forwards are traded over-the-counter.

Question 2

(Advanced) When interest rates and futures prices for an asset are uncorrelated and forwards are less liquid than futures, it is most likely that the price of a forward contract is:

A) less than the price of a futures contract.
B) equal to the price of a futures contract.
C) greater than the price of a futures contract.

Answer 2

B
Because gains and losses on futures contracts are settled daily, prices of forwards and futures that have the same terms may be different if interest rates are correlated with futures prices. When interest rates and futures prices are uncorrelated the prices of forward and futures on the same asset will be equal. Liquidity is not an issue as no-arbitrage prices are based on riskless hedges that are held until settlement of the derivative security.

Question 3

Fill in the blanks with either “futures” or “forwards”:
_____ are traded over-the-counter
_____ are traded on an exchange
_____ have lower counter risk (and why)

Answer 3

• forwards are traded over-the-counter.
• futures are traded on an exchange
• futures have lower counter risk (since it is traded on exchange and all futures positions are marked-to-market daily, with margins required to be posted and maintained by all participants at all times

Question 4

What is the definition of margin (for future contracts)

Answer 4

Margins are financial guarantees required of both buyers and sellers of futures contracts to ensure that they fulfill their futures contract obligations.

Question 5

Name the two types of margins and what is the difference between them

Answer 5

• Initial: Upon opening the futures position, an amount equal to the initial margin requirement will be deducted from the trader’s margin account and transferred to the exchange’s clearing firm.
• Maintenance: The maintenance margin is the minimum amount a futures trader is required to maintain in his margin account in order to hold a futures position. The maintenance margin level is usually slightly below the initial margin.

Question 6

Futures are ___ (more/less) valuable than forwards when interest rates and futures prices are positively correlated

Answer 6

more valuable

Question 7

If interest rates _____, the prices of futures and forwards are the same.

Answer 7

are constant or uncorrelated with futures prices

Question 8

(Intermediate) An option’s intrinsic value is equal to the amount the option is:

A) out of the money, and the time value is the market value minus the intrinsic value.
B) in the money, and the time value is the intrinsic value minus the market value.
C) in the money, and the time value is the market value minus the intrinsic value.

Answer 8

C
Intrinsic value is the amount the option is in the money. In effect it is the value that would be realized if the option were at expiration. Prior to expiration, the option’s market value will normally exceed its intrinsic value. The difference between market value and intrinsic value is called time value.

Question 9

(Intermediate) Which of the following will increase the value of a call option?

A) A dividend on the underlying asset.
B) An increase in the exercise price.
C) An increase in volatility.

Answer 9

C
Increased volatility of the underlying asset increases both put values and call values.
A or B - A higher exercise price or an increase in cash flows on the underlying asset decrease the value of a call option.
*increase in cashflow/dividend could be seen as benefit of holding an underlying assets

Question 10

Increase in Price of underlying asset will ____call option values and ____ put option values

Answer 10

Increase; Decrease

Question 11

Increase in exercise price will ____call option values and ____ put option values

Answer 11

Decrease; Increase

Question 12

Increase in Riskfree rate will ____call option values and ____ put option values

Answer 12

Increase; Decrease

Question 13

Increase in volatility of underlying asset will ____call option values and ____ put option values

Answer 13

Increase; Increase

Question 14

Increase in Time to expiration will ____call option values and ____ put option values

Answer 14

Increase; Increase (except some

European puts)

Question 15

Increase in Costs of holding underlying asset will ____call option values and ____ put option values

Answer 15

Increase; Decrease

think dividend and interest payments

Question 16

Increase in Benefits of holding underlying asset will ____call option values and ____ put option values

Answer 16

Decrease; Increase

Question 17

Name factors that will increase value of call options

5 and 2

Answer 17

increase in:

• Price of underlying asset
• Risk-free rate
• Volatility of underlying asset
• Time to expiration
• Costs of holding underlying asset

decrease in:

• Exercise price
• Benefits of holding underlying asset

Question 18

(Intermediate) A fiduciary call is a portfolio that is made up of:

A) a call option and a share of stock.
B) a call that is synthetically created from other instruments.
C) a call option and a bond that pays the exercise price of the call at option expiration.

Answer 18

C

A fiduciary call combines a call option and a bond that pays the exercise price of the call at option expiration.

Question 19

_____ and ______ have the same payoffs at expiration

Answer 19

fiduciary call and a protective put

Question 20

A fiduciary call is ______

Answer 20

A fiduciary call is a call option and a risk-free zero-coupon bond that pays the strike price X at expiration

Question 21

A ____ is a call option and a risk-free zero-coupon bond that pays the strike price X at expiration

Answer 21

fiduciary call

Question 22

(Advanced) A one-period binomial model is useful for valuing options because it:

A) can account for contingent payoffs of options.
B) considers the additional risk inherent in options.
C) does not require an assumption about volatility.

Answer 22

A
Binomial models are used to value options because they can account for contingent payoffs (i.e., the exercise value after an up-move or down-move in the underlying asset price).
C - The size of an up-move in a binomial model represents an assumption about the volatility of the underlying asset price.
B - Binomial models can use risk-neutral pseudo-probabilities and thereby use the risk-free rate to discount the expected future payoff.

Question 23

(Basic) A put option is in the money when:

A) the stock price is lower than the exercise price of the option.
B) there is no put option with a lower exercise price in the expiration series.
C) the stock price is higher than the exercise price of the option.

Answer 23

A

The put option is in-the-money if the stock price is below the exercise price.

Question 24

(Advanced) A synthetic European put option includes a short position in:

A) the underlying asset.
B) a European call option.
C) a risk-free bond.

Answer 24

A
A synthetic European put option consists of a long position in a European call option, a long position in a risk-free bond that pays the exercise price on the expiration date, and a short position in the underlying asset.

Question 25

A synthetic European put option consists of?

Answer 25

• a long position in a European call option,
• a long position in a risk-free bond that pays the exercise price on the expiration date,
• and a short position in the underlying asset.

Question 26

(Intermediate) The underlying instrument in a forward rate agreement is:

A) a fixed-income security.
B) an asset.
C) an interest rate.

Answer 26

C
A forward rate agreement is a forward contract with an interest rate, such as 30-day LIBOR, as its underlying instrument.

Question 27

(Intermediate) If the price of a forward contract is greater than the price of an identical futures contract, the most likely explanation is that:

A) the forward contract is more liquid.
B) the futures contract is more difficult to exit.
C) the futures contract requires daily settlement.

Answer 27

C
The reason there may be a difference in price between a forward contract and an identical futures contract is that a futures position has daily settlement and so makes or requires cash flows during its life.

Question 28

(Basic) When calculating the payoff for a stock option, if the stock price is greater than the strike price at expiration:

A) a call option expires worthless.
B) the payoff to a put option is equal to the strike price.
C) the payoff to a call option is the difference between the stock price and the strike price

Answer 28

C
If the stock price is greater than the strike price at expiration, the payoff to a call option on the stock equals the stock price minus the strike price, while a put option on the stock expires worthless.

Question 29

Think about the call-put parity: Fo(T) = So(1+Rf)^t
What should investor do when left is greater than right?
- forward
- underlying asset
- loan

Answer 29

Since left is greater, so you should want to get money at Fo in the future:
- Short the forward (so you can get the amount in the future),
- Borrow money at Rf and use the proceed to buy the asset.
~~ At time T, sell assets at Fo, pay back the proceed. Keep the difference

Question 30

Think about the call-put parity: Fo(T) = So(1+Rf)^t
What should investor do when left is smaller than right?
- forward
- underlying asset
- loan

Answer 30

Since left is smaller, you should want to get the money at So (compounded at Rf) in the future
- Short the asset at So, and then invest the proceed at Rf.
- Long a forward contract for Fo
~~At time T, receive the invested proceed and extra return: So (1+Rf)^t, pay Fo to buy the asset in order to cover the forward contract

Question 31

(Intermediate) An analyst is determining the value of a put option with a one-period binomial model. Using an up-move size of 25% and a risk-free rate of 3%, the analyst calculates the following:

Down-move size = 0.80
Up-move probability = 0.51
Down-move probability = 0.49
Value after up-move = $1.07
Value after down-move = $5.01
Probability-weighted average = 0.51($1.07) + 0.49($5.01) = $3.00

The analyst should determine that the value of the put option is:

A) less than $3.00.
B) equal to $3.00.
C) greater than $3.00.

Answer 31

A
The probability-weighted average is an estimate of the option’s expected value after one period. To determine the option’s value the analyst must discount this expected value by one period.

Question 32

(Intermediate) Which of the following most accurately states an example of replication in derivatives pricing?

A) Risky asset + risk-free asset = (- derivative position).
B) Risky asset + derivative = risk-free asset.
C) Derivative position - risk-free asset = risky asset.

Answer 32

B
Replications of future payoffs, composed of a risky asset, a risk-free asset, and a derivative on the risky asset, are as follows:

• Risky asset + derivative = risk-free asset
• Risky asset - risk-free asset = (- derivative position)
• Derivative position - risk-free asset = (- risky asset).

Question 33

(Advanced) A net benefit from holding the underlying asset of a forward contract will:

A) increase the value of the forward contract during its life.
B) decrease the value of the forward contract at expiration.
C) decrease the no-arbitrage forward price at initiation.

Answer 33

C
F0(T) = [S0 + PV0 (cost) - PV0 (benefit)] (1 + Rf )T
Compared to an underlying asset with no net holding cost or benefit, a net benefit from holding the underlying asset will decrease the no-arbitrage forward price at initiation and the value of a forward contract during its life. Holding costs and benefits have no effect on the value of a forward contract at expiration.
**benefit of holding – decrease the incentive to trade – decrease the value of forwards

Question 34

(Intermediate) Using put-call parity, it can be shown that a synthetic European call can be created by a portfolio that is:

A) long the stock, long the put, and long a pure discount bond that pays the exercise price at option expiration.
B) long the stock, long the put, and short a pure discount bond that pays the exercise price at option expiration.
C) long the stock, short the put, and short a pure discount bond that pays the exercise price at option expiration.

Answer 34

B
A stock and a put combined with borrowing the present value of the exercise price will replicate the payoffs on a call at option expiration.

*parity formula is fiduciary call = protected put
call + bond = put + stock
call = put and stock - bond
so long put, long stock, short bond

Question 35

What is a protected put?

Answer 35

Protected put is a share of stock and a put option on the stock

Question 36

What is the formula for European call-put parity?

Answer 36

fiduciary call = protected put

call + bond = put + stock

Question 37

(Basic) Greater volatility in the price of the underlying asset will have what effect on the value of a call option and the value of a put option?

  Value of a call option	Value of a put option A)             Increase	                        Decrease B)             Increase	                        Increase C)             Decrease	                Increase

Answer 37

B
Greater volatility in the price of the underlying asset increases the values of both puts and calls because options are “one-sided.” Since an option’s value can fall no lower than zero (it expires out of the money), increased volatility increases an option’s upside potential but does not increase its downside exposure.

Question 38

(Intermediate) A decrease in the riskless rate of interest, other things equal, will:

A) decrease call option values and decrease put option values.
B) decrease call option values and increase put option values.
C) increase call option values and decrease put option values.

Answer 38

B
(think present value using risk free rate. Call holder will pay money from using call in the future, so lower rate will make discounted cf higher ==> decrease value)

A decrease in the risk-free rate of interest will decrease call option values and increase put option values.

Question 39

(Advanced) Other things equal, the no-arbitrage forward price of an asset will be higher if the asset has:

A) storage costs.
B) convenience yield.
C) dividend payments.

Answer 39

A (think of incentive to trade. If there is a benefit to hold the asset, less likely to trade, less value of forward contract)

Costs of holding an asset increase its no-arbitrage forward price. Benefits from holding the asset, such as dividends or convenience yield, decrease its no-arbitrage forward price.

Question 40

(Intermediate) The value of a forward or futures contract is:

A) equal to the spot price at expiration.
B) specified in the contract.
C) typically zero at initiation.

Answer 40

C
The value of a forward or futures contract is typically zero at initiation, and at expiration is the difference between the spot price and the contract price. The price of a forward or futures contract is defined as the price specified in the contract at which the two parties agree to trade the underlying asset on a future date.

Question 41

(Intermediate) A call option that is in the money:

A) has an exercise price less than the market price of the asset.
B) has a value greater than its purchase price.
C) has an exercise price greater than the market price of the asset.

Answer 41

A

A call option is in the money when the exercise price is less than the market price of the asset.

Question 42

(Advanced) The calculation of derivatives values is based on an assumption that:

A) arbitrage opportunities are exploited rapidly.
B) investors are risk neutral.
C) arbitrage opportunities do not arise in real markets.

Answer 42

A (picked B)
Derivatives valuation is based on the assumption that any arbitrage opportunities in financial markets are exploited rapidly so that assets with identical cash flows are forced toward the same price. It does not assume arbitrage opportunities do not arise or that investors are risk neutral.
*Valuation of derivatives is based on a no-arbitrage condition with risk-neutral pricing.

Question 43

What are the conditions for valuation of derivatives?

Answer 43

• no-arbitrage condition (assumption that any arbitrage opportunities in financial markets are exploited rapidly)
• risk-neutral pricing (not risk neutral investors)

Question 44

(Intermediate) At expiration, the value of a European call option is:

A) less than that of an otherwise identical American call option.
B) equal to the asset price minus the present value of the exercise price.
C) equal to its intrinsic value.

Answer 44

C
The intrinsic value of a call, either European or American, at expiration is Max (0, S - X), which is its intrinsic value. The asset price minus the present value of the exercise price can be negative, but options cannot have a negative value.

Question 45

(Intermediate) James Anthony has a short position in a put option with a strike price of $94. If the stock price is below $94 at expiration, what will happen to Anthony’s short position in the option?

A) He will have the option exercised against him at $94 by the person who is long the put option.
B) He will let the option expire.
C) The person who is long the put option will not exercise the put option.

Answer 45

A
Anthony has sold the right to sell the stock at $94. That is, he received a payment upfront for the payer to have the right but not the obligation to sell the stock at $94. Because the option is in-the-money at expiration, MAX (0, X-S), the holder will exercise his right to sell at $94.

Question 46

What is the formula for put-call-forward purity?

Answer 46

change out the So with forward contract discounted to present value:
Fo/(1+Rf)^t+p = c+X/(1+Rf)^t

Question 47

(Advanced) The relationship referred to as put-call-forward parity states that at time = 0, if there is no arbitrage opportunity, the value of a call at X on an asset that has no holding costs or benefits plus the present value of X is equal to:

A) the asset price minus the value of a put option at X.
B) the value of a put option at X plus the present value of the forward contract price.
C) the forward contract price plus the value of a put option at X.

Answer 47

B
The put-call-forward parity relationship is:

c0 + X/(1 + Rf)T = p0 + F0(T)/(1 + Rf)T

The value of a call at X plus the present value of X is equal to the value of a put option at X plus the present value of the forward contract price.

Question 48

(Intermediate) The most likely use of a forward rate agreement is to:

A) exchange a floating-rate obligation for a fixed-rate obligation.
B) lock in an interest rate for future borrowing or lending.
C) obtain the right, but not the obligation, to borrow at a certain interest rate.

Answer 48

B
The purpose of a forward rate agreement (FRA) is to lock in an interest rate for future borrowing or lending. An FRA is a forward commitment rather than a contingent claim. An interest rate swap is used to exchange a floating-rate obligation for a fixed-rate obligation.

Question 49

(Intermediate) Given the following data regarding Printer, Inc.’s call options, which of the following statements is least accurate?

Stock Price Expiration Strike Option Prem. (Last)
50 June 45 6
50 June 50 2
50 June 55 0.50

A) The June $45.00 call is an in-the-money option.
B) The intrinsic value of the June $45.00 call is $5.00.
C) The June $55.00 call is an in-the-money option.

Answer 49

B
The June $55.00 call option is out-of-the money. It gives the purchaser the right to buy Printer, Inc. for $55.00 when they would only have to pay $50.00 in the market.

Question 50

(Intermediate) Bidco Corporation common stock has a market value of $30.00. Which statement about put and call options available on Bidco common is most accurate?

A) A put with a strike price of $35.00 is in-the-money.
B) A put with a strike price of $20.00 has intrinsic value.
C) A call with a strike price of $25.00 is at-the-money.

Answer 50

A
A put is in-the-money when its exercise price is higher than the market value of the underlying asset. A put with a $35.00 strike price allows the trader to sell 100 shares of stock for $35.00 per share, which is $5.00 higher than the prevailing market value. This gives the put a value, hence, it is in-the-money. For a call to be in-the-money, its strike price would have to be lower than the market value of the underlying common stock, allowing the trader to purchase 100 shares at a price below the prevailing market value. At-the-money is when the strike price and asset market value are equal. A put with a strike price of $20.00 does not have intrinsic value because it is below the $30 price of the stock. It does have time value meaning it is worth something because there is the possibility the put will come into the money before it expires.

Question 51

(Intermediate) The intrinsic value of an option is equal to:

A) the amount that it is in or out of the money.
B) zero or the amount that it is in the money.
C) its speculative value.

Answer 51

B
The intrinsic value of an option is equal to the amount that it is in the money or zero, if it is out of the money. Option value equals speculative (time) value only for out-of-the-money options.

Question 52

What is the intrinsic value of an option

Answer 52

The intrinsic value of an option is equal to the amount that it is in the money or zero

Question 53

(Advanced) Compared to an American call option on a stock that does not pay a dividend, an otherwise identical European call option will have:

A) a lower value.
B) a higher value.
C) the same value.

Answer 53

C
For call options on an underlying asset that does not pay cash flows, the right to exercise early is not valuable and therefore American and European options that are otherwise identical will have the same value.

Question 54

(Intermediate) During its life the value of a long position in a forward or futures contract:

A) is opposite to the value of the short position.
B) is equal to the value of the short position.
C) can differ in size from the value of the short position.

Answer 54

A
The long and short positions in a forward or futures contract have opposite values. A gain for one is an equal-sized loss for the other.

Question 55

(Intermediate) Which of the following is a nonmonetary benefit of holding an asset?

A) Dividends.
B) Convenience yield.
C) Storage and insurance.

Answer 55

B
Convenience yield refers to the nonmonetary benefits of holding an asset. Dividends are a monetary benefit. Storage and insurance are costs of holding an asset.

Question 56

_____ refers to the nonmonetary benefits of holding an asset.

Answer 56

Convenience yield

Question 57

Convenience yield refers to _____ of holding an asset.

Answer 57

the nonmonetary benefits

Question 58

(Intermediate) Consider a put option on Deter, Inc., with an exercise price of $45. The current stock price of Deter is $52. What is the intrinsic value of the put option, and is the put option at-the-money or out-of-the-money?

     Intrinsic Value	Moneyness A)             $7  	              At-the-money B)             $0          	     Out-of-the-money C)             $7  	             Out-of-the-money

Answer 58

B
The option has an intrinsic value of $0, because the stock price is above the exercise price. Put value is MAX (0, X-S). Equivalently, the option is out-of-the-money.

Question 59

(Intermediate) A European call option on a stock has an exercise price of 42. On the expiration date, the stock price is 40. The value of the option at expiration is:

A) zero.
B) positive.
C) negative.

Answer 59

A
For a call option, the value at expiration is zero if the price of the underlying is less than or equal to the exercise price. The holder will allow the option to expire unexercised.

Question 60

(Intermediate) As a forward contract approaches its expiration date, its value:

A) depends on the price of the underlying asset.
B) increases to the forward contract price.
C) approaches zero.

Answer 60

A
The value of a forward contract is zero at initiation, and during its life its value depends on changes in the spot price of the underlying asset. At expiration its value is based on the difference between the spot price of the underlying asset and the price specified in the forward contract.

Question 61

(Advanced) The price of a pay-fixed receive-floating interest rate swap is:

A) determined by expected future short-term rates.
B) zero when floating rates and fixed rates are equal.
C) negative when floating rates are highly volatile.

Answer 61

A
The price of an interest rate swap refers to the fixed rate specified in the swap. This price is calculated as a function of expected future short-term rates.

Question 62

The ____ of a swap is the fixed rate of interest specified in the swap contract. The ____ depends on how expected future floating rates change over time.

Answer 62

price; price

Question 63

An increase in expected short-term future rates will produce a ____ (positive/negative) value for the fixed-rate payer,

Answer 63

positive

Question 64

The price of a swap is ______. The value _____

Answer 64

• fixed rate of interest specified in the swap contract.

- depends on how expected future floating rates change over time.

Question 65

(Advanced) An increase in the riskless rate of interest, other things equal, will:

A) increase call option values and decrease put option values.
B) decrease call option values and decrease put option values.
C) decrease call option values and increase put option values.

Answer 65

A

An increase in the risk-free rate of interest will increase call option values and decrease put option values.

Question 66

(Intermediate) Basil, Inc., common stock has a market value of $47.50. A put available on Basil stock has a strike price of $55.00 and is selling for an option premium of $10.00. The put is:

A) in-the-money by $7.50.
B) out-of-the-money by $2.50.
C) in-the-money by $10.00.

Answer 66

A
(no need to consider the price of the option)
The put allows a trader to sell Basil common stock for $7.50 more than the current market value ($55.00 − $47.50). The trade is normally closed out with a cash settlement, but the trader could buy 100 shares for $47.50 per share and immediately sell them to the option writer for $55.00.

Question 67

(Intermediate) On the expiration date of a European put option, if the spot price of the underlying asset is less than the exercise price, the value of the option is:

A) negative.
B) positive.
C) zero.

Answer 67

B
Put options are in the money (have positive value) at expiration if the spot price of the underlying asset is less than the exercise price, because the put option holder has the right to sell the asset for the higher exercise price. The value of an option cannot be negative; at expiration its value is the greater of zero or its intrinsic value.

Question 68

(Advanced) A synthetic European call option includes a short position in:

A) the underlying asset.
B) a risk-free bond.
C) a European put option.

Answer 68

B
A synthetic European call option consists of a long position in the underlying asset, a long position in a European put option, and a short position in a risk-free bond (i.e., borrowing at the risk-free rate).
*call + bond = put + stock
call = put + stock - bond

Question 69

(Advanced) It is possible to profit from arbitrage when there are no costs or benefits to holding the underlying asset and the forward contract price is:

A) less than the future value of the spot price.
B) less than the present value of the spot price.
C) greater than the present value of the spot price.

Answer 69

A
An opportunity for arbitrage exists if the forward price is not equal to the future value of the spot price, compounded at the risk-free rate over the period of the forward contract.

forward = spot (1+rf)^t

Question 70

(Advanced) Compared to European put options on an asset, otherwise identical American put options on the asset are most likely to be more valuable if:

A) the options are out-of-the-money.
B) the asset pays dividends during the life of the option.
C) the asset value is significantly lower than the exercise price.

Answer 70

C
Early exercise of an in-the-money American put option is valuable when the asset value is significantly below the exercise price (i.e. they are deep in-the money). The payment of interest or dividends from the underlying asset increases put values, so it does not make early exercise valuable as it does with call options.

Question 71

(Basic) An investor would exercise a put option when the:

A) price of the stock is below the strike price.
B) price of the stock is equal to the strike price.
C) price of the stock is above the strike price.

Answer 71

A
A put option gives its owner the right to sell the underlying good at a specified price (strike price) for a specified time period. When the stock’s price is less than the strike price a put option has value and is said to be in-the-money.

Question 72

(Advanced) The price of a fixed-for-floating interest rate swap contract:

A) is established at contract initiation.
B) is directly related to changes in the floating rate.
C) may vary over the life of the contract.

Answer 72

A
The price of a swap contract is set such that the contract has a value of zero at initiation. The value of a fixed-for-floating interest rate swap contract may vary over its life as the floating rate changes.

Question 73

(Basic) A forward rate agreement (FRA):

A) is settled by making a loan at the contract rate.
B) can be used to hedge the interest rate exposure of a floating-rate loan.
C) is risk-free when based on the Treasury bill rate.

Answer 73

B
An FRA settles in cash and carries both default risk and interest rate risk, even when based on an essentially risk-free rate. It can be used to hedge the risk/uncertainty about a future payment on a floating rate loan.

Question 74

(Advanced) For two European put options that differ only in their time to expiration, which of the following is most accurate? The longer-term option:

A) is worth more than the shorter-term option.
B) can be worth less than the shorter-term option.
C) is worth at least as much as the shorter-term option.

Answer 74

B
For European puts, it is possible that the longer term option can be less valuable than a shorter-term option.
(normally longer term = more value for put. This does not affect call)

Question 75

(Advanced) For an underlying asset that has no holding costs or benefits, the no-arbitrage forward price at initiation of a forward contract is:

A) zero.
B) equal to the spot price.
C) the future value of the spot price.

Answer 75

C
At initiation of a forward contract on an underlying asset with no holding costs or benefits, the no-arbitrage forward price is the future value of the spot price, compounded at the risk-free rate to the expiration date of the forward contract: Fo(T) = S0(1 + Rf)T. The forward contract has a value of zero at initiation if the forward price in the contract is equal to the no-arbitrage forward price.

Question 76

(Intermediate) The payoff of a call option on a stock at expiration is equal to:

A) the maximum of zero and the stock price minus the exercise price.
B) the minimum of zero and the stock price minus the exercise price.
C) the maximum of zero and the exercise price minus the stock price.

Answer 76

A

The payoff on a call option on a stock is Max (0, S - X).

Question 77

(Advanced) Derivatives valuation is based on risk-neutral pricing because:

A) risk tolerances of long and short investors are assumed to offset.
B) the risk of a derivative is based entirely on the risk of its underlying asset.
C) this method provides an intrinsic value to which investors apply a risk premium.

Answer 77

B
Because the risk of a derivative is based entirely on the risk of its underlying asset, we can construct a perfectly hedged portfolio of a derivative and its underlying asset. The future payoff of a perfectly hedged position is certain and can therefore be discounted at the risk-free rate.

Question 78

(Intermediate) A call option’s intrinsic value:

A) increases as the stock price increases above the strike price, while a put option’s intrinsic value increases as the stock price decreases below the strike price.
B) decreases as the stock price increases above the strike price, while a put option’s intrinsic value increases as the stock price decreases below the strike price.
C) increases as the stock price increases above the strike price, while a put option’s intrinsic value decreases as the stock price decreases below the strike price.

Answer 78

A
For a call option, as the underlying stock price increases above the strike price, the option moves farther into the money, and the intrinsic value is increasing. For a put option, as the underlying stock price decreases below the strike price, the option moves farther into the money, and the intrinsic value is increasing.

Question 79

(Basic) One of the principal characteristics of swaps is that swaps:

A) are standardized derivative instruments.
B) may be likened to a series of forward contracts.
C) are highly regulated over-the-counter agreements.

Answer 79

B
A swap agreement often requires that both parties agree to a series of transactions. Each transaction is similar to a forward contract, where a party is paying a fixed price to offset the risk associated with an unknown future value.
C - Swaps are over-the-counter agreements but are not highly regulated.
A - One of the benefits of swaps is that they can be customized to fit the needs of the counterparties. Thus, they are not standardized.

Question 80

(Advanced) For an underlying asset that has no holding costs or benefits, the value of a forward contract to the long during the life of the contract is the:

A) spot price minus the present value of the forward price.
B) difference between the spot price and the forward price.
C) present value of the difference between the spot price and the forward price.

Answer 80

A
During the life of a forward contract on an underlying asset with no holding costs or benefits, the value to the long equals the spot price minus the present value of the forward price:

Vt(T) = St - F0(T) / (1 + Rf)T-t.

Question 81

(Intermediate) Which of the following statements about moneyness is most accurate? When the stock price is:

A) above the strike price, a put option is in-the-money.
B) above the strike price, a put option is out-of-the-money.
C) below the strike price, a call option is in-the-money.

Answer 81

B
When the stock price is above the strike price, a put option is out-of-the-money.
When the stock price is below the strike price, a call option is out-of-the-money.

Question 82

(Intermediate) If futures prices are positively correlated with interest rates, futures prices will be:

A) unaffected relative to forward prices.
B) less than forward prices.
C) greater than forward prices.

Answer 82

C
Futures prices will be greater than forward prices if interest rates are positively correlated with futures prices, because daily settlement of long futures positions will produce excess margin when interest rates are high and require margin deposits when interest rates are low.

Question 83

(Intermediate) At expiration, the value of a call option is the greater of zero or the:

A) underlying asset price minus the exercise value.
B) underlying asset price minus the exercise price.
C) exercise price minus the exercise value.

Answer 83

B

The value of a call option at expiration is its exercise value, which is Max[0, S - X].

Question 84

(Advanced) For a series of forward contracts to replicate a swap contract, the forward contracts must have:

A) values at swap expiration that sum to zero.
B) values at swap initiation that sum to zero.
C) values at swap initiation that are equal to zero.

Answer 84

!!B
When replicating a swap with a series of forward contracts, each forward contract is likely to be off-market (i.e., have a non-zero value at initiation), but they can replicate a swap with a value of zero at initiation if the values of the forward contracts sum to zero at swap initiation.

Question 85

(Intermediate) Which of the following is typically equal to zero at the initiation of an interest rate swap contract?

A) Its price.
B) Its value.
C) Neither its value nor its price.

Answer 85

B
As with other derivatives, the price of an interest rate swap (the fixed rate specified in the contract) is typically set such that the value of the swap is zero at initiation.

Question 86

(Advanced) Which of the following instruments is a component of the put-call-forward parity relationship?

A) The spot price of the underlying asset.
B) The present value of the forward price of the underlying asset.
C) The future value of the forward price of the underlying asset.

Answer 86

B
The put-call-forward parity relationship is: F0(T) / (1 + RFR)T + p = c + X / (1 + RFR)T, where F0(T) is the forward price of the underlying asset.

Question 87

(Intermediate) Using put-call parity, it can be shown that a synthetic European put can be created by a portfolio that is:

A) long the stock, short the call, and short a pure discount bond that pays the exercise price at option expiration.
B) short the stock, long the call, and short a pure discount bond that pays the exercise price at option expiration.
C) short the stock, long the call, and long a pure discount bond that pays the exercise price at option expiration.

Answer 87

C
A short position in the stock combined with a long call and lending the present value of the exercise price will replicate the payoffs on a put at option expiration
*parity formula is fiduciary call = protected put
call + bond = put + stock
put = call + bond - stock
so long call, long bond, short stock

Question 88

(Intermediate) Dividends or interest paid by the asset underlying a call option:

A) increase the value of the option.
B) have no effect on the value of the option.
C) decrease the value of the option.

Answer 88

C
Dividends or interest paid by the underlying asset decrease the value of call options.
(and increase put option value)

Question 89

(Basic) Which of the following statements about long positions in put and call options is most accurate? Profits from a long call:

A) and a long put are positively correlated with the stock price.
B) are negatively correlated with the stock price and the profits from a long put are positively correlated with the stock price.
C) are positively correlated with the stock price and the profits from a long put are negatively correlated with the stock price.

Answer 89

C
For a call, the buyer’s (or the long position’s) potential gain is unlimited. The call option is in-the-money when the stock price (S) exceeds the strike price (X). Thus, the buyer’s profits are positively correlated with the stock price. For a put, the buyer’s (or the long position’s) potential gain is equal to the strike price less the premium. A put option is in-the-money when X > S. Thus, a put buyer wants a high exercise price and a low stock price. Thus, the buyer’s profits are negatively correlated with the stock price.

Question 90

(Advanced) Consider a European call option and put option that have the same exercise price, and a forward contract to buy the same underlying asset as the two options. An investor buys a risk-free bond that will pay, on the expiration date of the options and the forward contract, the difference between the exercise price and the forward price. According to the put-call-forward parity relationship, this bond can be replicated by:

A) writing the call option and writing the put option.
B) writing the call option and buying the put option.
C) buying the call option and writing the put option.

Answer 90

B
The put-call-forward parity relationship may be expressed as:

p0 - c0 = [X - F0(T)] / (1 + Rf)T
That is, at initiation of a forward contract on the underlying asset, buying a put option and writing a call option with exercise price X will have the same cost as a risk-free bond which, at expiration of the forward and options, will pay the difference between X and the forward price.

Question 91

(Advanced) Bea Moran wants to establish a long derivatives position in a commodity she will need to acquire in six months. Moran observes that the six-month forward price is 45.20 and the six-month futures price is 45.10. This difference most likely suggests that for this commodity:

A) long investors should prefer futures contracts to forward contracts.
B) futures prices are negatively correlated with interest rates.
C) there is an arbitrage opportunity among forward, futures, and spot prices.

Answer 91

B
Differences may exist between forward and futures prices for otherwise identical contracts if futures prices are correlated with interest rates. If futures prices are negatively correlated with interest rates, daily settlement of long futures contracts will require cash when interest rates are increasing and produce cash when interest rates are decreasing. As a result the futures price will be lower than the forward price. The difference in price does not provide an arbitrage opportunity or suggest that investors should prefer forward or futures contracts.

Question 92

(Basic) Which of the following statements about American and European options is most accurate?

A) Prior to expiration, an American option may have a higher value than an equivalent European option.
B) There will always be some price difference between American and European options because of exchange-rate risk.
C) European options allow for exercise on or before the option expiration date.

Answer 92

A
American and European options both give the holder the right to exercise the option at expiration. An American option also gives the holder the right of early exercise, so American options will be worth more than European options when the right to early exercise is valuable, and they will have equal value when it is not.

Question 93

Difference between American and European options?
When will American call be more valuable than European call?
what about for put?

Answer 93

American options allow early exercising

• For a call option: If the asset pays cash flows during the life of a call option, early exercise can be valuable and an American call option will be priced higher than an otherwise identical European call option.
• For put options, early exercise can be valuable when the options are deep in the money and an American put option will be priced higher than an otherwise identical European put option.