Deck 19: Exotic Options II: Path-Dependent Options

Question 1

Consider a floating-strike lookback put option written on a stock.Let $S ^ { \mathrm { max } }$ and $S ^ { \mathrm { min } }$ denote the maximum and minimum prices of the stock over the option's life.Then,the payoff to the option holder is given by $\max \{ X - Y , 0 \}$ ,where

A) $X = S ^ { \max }$
And
$Y = K$
,the given strike price of the option.
B) $X = K$
And
$Y = S ^ { \text {min } }$
)
C) $X = S ^ { \max }$
And
$Y = S _ { T }$
,the price of the underlying at maturity.
D) $X = S _ { T }$
And
$Y = S ^ { \text {min } }$
)

Answer 1

$X = S ^ { \max }$
And
$Y = S _ { T }$
,the price of the underlying at maturity.

Question 2

A cliquet is analogous to

A)A portfolio of vanilla options,all at-the-money today,and expiring on the reset dates of the cliquet.
B)A portfolio of digital options,with one option coming to life at each reset date and expiring at the next reset date.
C)A portfolio of forward-starts,with one option coming to life at each reset date and expiring at the next reset date.
D)A portfolio of exchange options,with one option coming to life at each reset date and expiring at the next reset date.

Answer 2

C

Question 3

In a barrier option,

A)Price paths are bounced off the barrier.
B)Option payoffs are conditional on whether the underlying breached the barrier during the option's life.
C)Option payoffs are conditional on when the underlying breached the barrier during the option's life.
D)Conditional on the barrier being breached during the option's life,option payoffs differ based on how many times the barrier was breached.

Answer 3

B
Choice (a)is nonsense.Choice (b)is the definition of a barrier option.When the barrier was breached is not relevant,only that it was breached.The payoff is the same no matter how many times the barrier was breached.

Question 4

You hold a fixed-strike lookback put option written on a stock that was at-the-money at inception.The stock price at inception was $56,the stock price at maturity is $63,and the lowest and highest stock prices observed over the option's life are,respectively,$52 and $64.The payoff from the option at maturity is

A)Zero.
B)$4.
C)$8.
D)$11.

Question 5

If you buy a knock-out call option with barrier $H$ satisfying $H > K = S$ where $K$ and $S$ are the strike price and current price of the underlying,respectively,then your implied view of prices is that

A)Prices are going up to at least the level of the barrier.
B)Prices are going up,but at most to the level of the barrier.
C)Prices are moving down.
D)Prices may move up to the level of the barrier before moving down.

Question 6

Consider a down-and-out call and a down-and-in call with a current stock price $S$ ,barrier $H < S$ ,and strike $K > H$ .When does the knock-out option increase in price and the knock-in decrease in price?

A)When the stock price increases.
B)When the volatility increases.
C)When the barrier increases.
D)When the strike increases.

Question 7

A number of companies were accused of "backdating" executive stock options in the 2000s.Backdating is the procedure by which companies chose the date on which the stock was was most favorable (i.e. ,at its lowest)to act as the putative start date of the option grant.By permitting backdating,companies were essentially giving their executives a form of a

A)Cliquet option.
B)Shout option.
C)Floating-strike lookback option.
D)Fixed-strike lookback option.

Question 8

An option is said to be path-dependent if

A)It has a payoff that depends in some way on the path of prices taken by the underlying.
B)It can only be priced on a non-recombining tree.
C)Different paths of the asset price necessarily lead to different payoffs.
D)All of the above.

Question 9

The USD/GBP exchange rate is $1.575/ $f$ .An investor buys a knock-out USD call/GBP put with a strike of $1.575/ $f$ and a barrier of $1.515/ $£$ .The implied view of the investor is

A)GBP is going to appreciate against the dollar by at least $0.06/ $£$
)
B)GBP is going to appreciate against the dollar but by at most $0.06/ $£$
)
C)GBP is going to depreciate against the dollar by at least $0.06/ $£$
)
D)GBP is going to depreciate against the dollar but by at most $0.06/ $£$
)

Question 10

In the 1990s,a number of companies which had experienced sharp stock price declines,"repriced" previously-awarded employee stock options.Repricing consisted of resetting the options' strike prices to the current stock price (so as to bring them closer to the money).Suppose a company awards at-the-money stock options to its employees and decides it will reprice them if the stock price falls 50% from the initial award date.Then,the employee stock option is equivalent to a portfolio of

A)A vanilla call and a forward-starting call.
B)A knock-out and a knock-in barrier call option.
C)A knock-out call and a forward-strarting call.
D)A cliquet.

Question 11

Assuming no rebates upon knock-out,a down-and-out call option is worth less than a vanilla call

A)When the knock-out barrier lies above the current stock price.
B)When the knock-out barrier lies below the current stock price.
C)When the knock-out barrier is far from the strike price.
D)Always.

Question 12

Given a current stock price $S$ ,strike price $K$ ,and barrier $H$ ,which of the following statements is most valid?

A)Given $H < K < S$
,if the barrier
$H$
Is moved lower,then a down-and-in put increases in value and a down-and-out put falls in value.
B)Given $H < S < K$
,if the barrier
$H$
Is moved lower,then a down-and-in put and a down-and-out put both increase in value.
C)Given $H < K < S$
,if the barrier
$H$
Is moved lower,then a down-and-out call increases in value and a down-and-in call decreases in value.
D)Given $H < K < S$
,if the barrier
$H$
Is moved lower,then a down-and-out call and a down-and-in call both increase in value.

Question 13

When volatility increases,the value of a down-and-out put ,and the value of a down-and-in put.

A)increases;increases.
B)decreases;increases.
C)may increase or decrease;increases.
D)decreases;may increase or decrease.

Question 14

A portfolio comprising an up-and-out put and an up-and-in put is equivalent to

A)A up-and-out call and a up-and-in call.
B)A vanilla call.
C)A down-and-out put and a down-and-in put.
D)A vanilla put

Question 15

A cliquet is equivalent to a family of forward starting options in which one option comes to life at each reset date and expires on the next reset date.A reverse cliquet

A)Is a portfolio of vanilla put options,all at-the-money today,and expiring on the reset dates of the reverse cliquet.
B)Is a portfolio of digital put options,with one option coming to life at each reset date and expiring at the next reset date.
C)Is a cliquet that runs in reverse,with options expiring at each reset date whose strike is determined only at the next reset date.
D)Has an identical structure to the cliquet but in which there is a promised fixed return at expiry that is reduced by the moneyness at expiry of each forward starting option in the cliquet.

Question 16

Consider an option that pays $1000 if the stock price at maturity falls outside a range $\left[ K _ { 1 } , K _ { 2 } \right]$ .Which of the following is valid?

A)The option may be written as the sum of two barrier options.
B)The option decreases in value as $K _ { 2 } - K _ { 1 }$
Decreases.
C)The option may be written as the sum of two asset-or-nothing options.
D)The option may be written as the sum of two cash-or-nothing options.

Question 17

Consider two paths A and B for stock prices in a barrier option setting that result in the same terminal price.Paths A and B will have different payoff consequences for the barrier option if

A)Path A crossed the barrier before maturity while Path B did not.
B)Both paths crossed the barrier prior to maturity but Path A re-crossed it while Path B did not.
C)Neither path crossed the barrier prior to maturity.
D)All of the above.

Question 18

You hold a floating-strike lookback put option written on a stock.The stock price at inception was $56,the stock price at maturity is $63,and the lowest and highest stock prices observed over the option's life are,respectively,$52 and $64.The payoff from the option at maturity is

A)Zero.
B)$1.
C)$11
D)Cannot be answered without information on the strike price.

Question 19

Which of the following statements is accurate concerning knock-out call options?

A)The delta is positive if it is a down-and-out call but can be positive or negative if it is an up-and-out call.
B)The delta can be positive or negative,but the gamma is always positive.
C)The delta is always positive,but the gamma can be positive or negative.
D)The delta can be positive or negative and the gamma can also be positive or engative.

Question 20

An up-and-out put may be preferred to a vanilla put

A)Because it results in higher payoffs in all circumstances.
B)Because it sometimes pays off even when the stock price rises whereas the vanilla only pays off when the stock price falls.
C)By an Investor with strong directional views because it is a cheaper form of taking on a directional bet.
D)By an investor more concerned with direction than volatility because the down-and-out put always reacts negatively to volatility unlike the vanilla put.

Question 21

Which of the following statements about backdating is most valid?

A)A backdated option is one that is issued prior to today.
B)Backdating usually involves the issuance of an option with a prior issue date and lower strike than today's price.
C)Backdating usually involves the ex-post issuance of an out-of-the-money option.
D)A backdated option is exactly the same as a fixed-strike lookback option.

Question 22

Which of the following statements is FALSE?

A)Asian calls are always worth less than the corresponding vanilla calls.
B)Asian puts are always worth less than the corresponding vanilla puts.
C)Arithmetic-average Asian calls are always worth less than the corresponding vanilla calls but geometric-average Asian calls may be worth more.
D)At low volatilities,all Asian options are worth less than the corresponding vanilla options,but at high volatilities they may be worth more.

Question 23

The delta of a up-and-out call option with barrier $H$ lying above the strike $K$ is most likely to be negative when

A)The underlying stock price $S$
Is at or near
$K$
)
B)The underlying stock price $S$
Is close to and less than
$H$
)
C)The underlying stock price $S$
Is well below
$K$
)
D)The delta of a call cannot be negative.

Question 24

The most valid relationship between the values of European calls ( $C _ { E }$ ),American calls ( $C _ { A }$ ),shout call options ( $C _ { S }$ ),and lookback calls ( $C _ { L }$ )is as follows:

A) $C _ { A } \leq C _ { S } \leq C _ { L }$
B) $C _ { E } \leq C _ { L } \leq C _ { S }$
C) $C _ { S } \leq C _ {E } \leq C _ { A }$
D) $C _ { A } \leq C _ { L } \leq C _ { S }$

Question 25

Which of the following statements is most valid?

A)Asian options are useful for hedging risk to markets in Asia.
B)Asian options are usually more expensive than vanilla options because they are exotic.
C)Asian options are useful for hedging exposure to the average price of a security or commodity.
D)Asian options are more sensitive to volatility than vanilla options.

Question 26

At inception,which of the following options would have the lowest value? Assume that the strike price of all the options is set equal to the current price of the underlying stock.

A)Arithmetic average Asian call option.
B)Geometric average Asian call option.
C)Vanilla European call.
D)Vanilla American call.

Question 27

A number of companies were accused of "backdating" executive stock options in the 2000s.Backdating is the procedure by which companies chose the date on which the stock was was most favorable (i.e. ,at its lowest)to act as the putative start date of the option grant.By permitting backdating,companies were essentially giving their executives a form of a

A)Cliquet option.
B)Shout option.
C)Floating-strike lookback option.
D)Fixed-strike lookback option.

Question 28

Cliquet options are purchased because

A)A portfolio of forward start options is cheaper than buying them separately.
B)There is diversification in a portfolio of forward start options.
C)They are analogous to owning Asian forward options.
D)It is the same as buying rolling forward start options but has the advantage of locking in possibly low volatilities today.

Question 29

An Asian option is an option where

A)The underlying is the average of the stock price for a specified period.
B)The strike price is the average of the stock price over a specified period.
C)The average can be an arithmetic or geometric average.
D)All of the above are possible in an Asian option.

Question 30

Consider the following at-the-money options,all of the same maturity: a vanilla European call ( $C _ { E }$ ),an American vanilla call ( $C _ { A }$ ),a fixed-strike lookback call ( $C _ { L }$ ).Which of the following is correct?

A) $C _ { L } \leq C _ {E } \leq C _ { A }$ .
B) $C _ { L } \leq C _ {E } \leq C _ { A }$
C) $C _ {E } \leq C _ { A } \leq C _ { L }$
D) $C _ { A } \leq C _ { E } \leq C _ { L }$ .

Question 31

A shout option

A)Is like a barrier option but in which the option holder gets to choose a barrier at any point.
B)Is effectively an American option which can be exercised at any time before maturity.
C)Is an option where you can lock-in "early-exercise" profits at any one point and receive,at maturity,the maximum of these locked-in profits or the moneyness of the option at maturity.
D)Is a Bermudan option with only one specified early-exercise date,that is,it can be exercised early on that given date or at maturity.

Question 32

When is an Asian option less useful than a vanilla option?

A)For reducing the incentives for price manipulation of the underlying close to maturity.
B)For making the option less sensitive to jump risk close to maturity.
C)For hedging exposure to the average price of a security.
D)For taking directional bets.

Question 33

In one type of a lookback option,

A)You can decide to change the option from a call to a put or vice versa at the last minute.
B)You can take any observed price prior to maturity as the strike of the option.
C)You can take the average observed price of the underlying in determining the option payoff.
D)The initial price of the underlying acts as the strike price of the option.