Deck 18: Path-Independent Exotic Options

Question 1

A path-independent option is
(a) An option where the price process is not continuous, i.e., it does not follow a smooth path, but jumps from one value to the next.
(b) An option where the option payoff depends on the price of the underlying asset at exercise time but not on the details of the price path followed to that point.
(c) An option where the option payoff is independent of anything that happens to the price of the underlying after inception.
(d) An option where the option payoff is constant regardless of the path taken by the price of the underlying.

Answer 1

B.

Question 2

A three-month at-the-money call option on a stock is trading at $5; the stock is trading at $50. A forward start option that comes to life in one month and has a life of three months from that point and that will be at-the-money when it comes to life is trading at $4.98. You hold a portfolio that is long the three-month call and short the forward start. The gamma of the portfolio is
(a) Positive
(b) Zero
(c) Negative
(d) Can be positive, zero, or negative.

Answer 2

A

Question 3

An exotic option is
(a) An option that is either A sian or Bermudan.
(b) An option that is unique and not widely traded.
(c) An option that is not a vanilla put or call.
(d) An option where there are more than two counterparties in the deal.

Answer 3

C.

Question 4

A cash-or-nothing binary call option increases in value when the price of the underlying increases. The delta of such an option
(a) Is positive and increases in value as the price of the underlying increases.
(b) can be positive or negative, but increases in value as the price of the underlying increases.
(c) is positive but can increase or decrease in value as the price of the underlying increases.
(d) is equal to the risk-neutral probability of the option finishing in-the-money.

Question 5

Consider a stock that pays no dividends. You hold a portfolio comprising an asset-or-nothing call and a cash-or-nothing put. The options share the same strike, and the cash-or-nothing put pays an amount equal to the strike price if the put finishes in-the-money. Your portfolio is equivalent to
(a) A vanilla call.
(b) A vanilla put.
(c) A covered call.
(d) A protective put.

Question 6

The gamma of a cash-or-nothing binary call option is generally when the option is out-of-the-money and generally when it is in-the-money.
(a) negative; positive.
(b) negative; negative.
(c) positive; negative.
(d) positive; positive.

Question 7

The gamma of a cash-or-nothing binary call option and the theta of such an option
(a) is always positive; is always negative.
(b) is always positive; can be positive or negative.
(c) can be positive or negative; is always negative.
(d) can be positive or negative; can be positive or negative.

Question 8

Consider digital (cash-or-nothing) call options. When volatility increases, the holders of out-of-the-money options generally , and the holders of in-the-money options generally
(a) benefit; benefit.
(b) benefit; lose.
(c) lose; benefit.
(d) lose; lose.

Question 9

At maturity in an asset-or-nothing option written on a stock,
(a) The holder has a choice of receiving the asset or nothing in exchange for paying the strike price.
(b) The holder receives the stock in exchange for the strike price if the option should finish in-the-money, and nothing otherwise.
(c) The holder receives the stock without paying anything in exchange if the option should finish in-the-money, and nothing otherwise.
(d) The holder receives the stock in exchange for a pre-specified consideration (which could differ from the strike price) if the option should finish in-the-money, and nothing otherwise.

Question 10

An exotic option is
(a) Any option written on an unusual or rare underlying asset.
(b) An option that is traded only by boutique organizations.
(c) Any option that is not a plain vanilla put or call.
(d) Any option with very complex payoff patterns.

Question 11

As maturity approaches, the delta of an at-the-money cash-or-nothing digital call option

A) Increases.
B) Decreases.
C) Remains constant.
D) Converges to a value of $1 / 2$ .

Question 12

You are long a portfolio of vanilla call options. Which of the following will help you hedge away your convexity (gamma)?
(a) Buying a portfolio of in-the-money vanilla put options.
(b) Buying a portfolio of out-of-the money vanilla put options.
(c) Buying a portfolio of in-the-money cash-or-nothing put options.
(d) Buying a portfolio of out-of-the money cash-or-nothing put options.

Question 13

Let $K$ denote the strike of an asset-or-nothing call option and $S _ { T }$ the price of the underlying at maturity. The option is worth

A) The present value of $S _ { T }$ taken over the region $S _ { T } \geq K$ .
B) The present value of $K$ taken over the region $S _ { T } \geq K$ .
C) $K$ times the risk-neutral probability of the option finishing in-the-money.
D) The present value of $S _ { F } - K$ taken over the region $S _ { T } \geq K$ .

Question 14

A cash-or-nothing call option written on a stock
(a) Pays the value of the stock in cash if the option finishes in-the-money and nothing otherwise.
(b) Pays a fixed amount of cash if the option finishes in-the-money and nothing otherwise.
(c) Is any cash-settled standard call option.
(d) Pays the difference between the stock price and strike price in cash to the option holder if the option should finish in-the-money and nothing otherwise.

Question 15

The delta of a cash-or-nothing call option is highest when the option is
(a) Deep out-of-the-money.
(b) At- or near-the-money.
(c) Deep in-the-money.
(d) 25% out-of-the-money.

Question 16

A forward-start option may be viewed as path-independent because
(a) The features of the option when it comes to life depend on the price of the underlying at that point but not on the path taken to reach that price.
(b) The payoff of the forward-start on its maturity date does not depend on any features of the price path of the underlying from the date of purchase of the option.
(c) A forward start option always starts irrespective of the path taken to the forward start date.
(d) Only the strike price of the option is unknown at the time of entering into the option.

Question 17

A forward-start option is
(a) An option where the strike is determined on a specified date in the future.
(b) An option where the strike is determined at an uncertain future date.
(c) An option where the life of the of the option is determined on a specified date in the future.
(d) An option that is at-the-money when it comes to life.

Question 18

A three-month at-the-money call option on a stock index is trading at $5; the index is trading at $50. A forward start option on the index that comes to life in one month, has a life of three months from that point and that will be at-the-money when it comes to life, is trading at $4.98. The one-month rate of interest is 2% in continuously-compounded and annualized terms. What is the one-month forward price of the index?
(a) $50.00
(b) $50.05
(c) $50.25
(d) $50.45

Question 19

Option prices are homogeneous of degree one in stock price and strike price. What does this imply?
(a) That if you double the stock price and the strike price the option price will remain unchanged.
(b) That if you double the stock price the option price will double.
(c) That if you double the stock price and halve the strike price the option price will double
(d) That if you double the stock price and strike price the option price will double.

Question 20

The delta of a cash-or-nothing binary call option and the gamma of such an option
(a) is always positive; is always positive.
(b) is always positive; can be positive or negative.
(c) can be positive or negative; is always positive.
(d) can be positive or negative; can be positive or negative.

Question 21

Which of the following compound options has a non-monotone delta function?
(a) A call on a call.
(b) A put on a put.
(c) Both (a) and (b).
(d) Neither (a) nor (b).

Question 22

A stock is trading at 100. Consider a two-period binomial model in which the stock price moves up or down each period by factors $u = 1.20$ and $d = 0.80$ , respectively. Suppose the gross risk-free rate of interest per time-step is 1.04. In this setting, the price of a two-period cash-or-nothing binary put option with a strike of 100 that pays $100 if it finishes in-the-money is

A) $36.
B) $33.28
C) $64.
D) $59.17.

Question 23

Consider pricing an exchange option on two stocks. Assume the usual lognormal returns distributions on the stock prices as in Magrabe's formula. Which of the following input variables does NOT affect the probability of the option being in-the-money at maturity?
(a) The volatility of the assets' returns.
(b) The risk-free rate.
(c) The correlation between the two assets' returns.
(d) The time to maturity of the option.

Question 24

Consider the following compound options written on an underlying stock. Which one decreases in value when the stock falls in price?
(a) A put on a call.
(b) A call on a put.
(c) A put on a put.
(d) None of the above.

Question 25

You are long a portfolio of vanilla call options. Which of the following will help you hedge away your theta risk?
(a) Buying a portfolio of in-the-money cash-or-nothing call options.
(b) Buying a portfolio of out-of-the money cash-or-nothing call options.
(c) Buying a portfolio of in-the-money vanilla call options.
(d) Buying a portfolio of out-of-the money vanilla call options.

Question 26

You are a UK-based investor who is interested in investing in options on Japanese stocks. The options are denominated in Japanese yen (JPY), but you are not interested in taking on GBP/JPY exchange-rate risk. The most suitable alternative for you is to
(a) Combine the options on Japanese stock with GBP/JPY foreign currency options.
(b) Combine the options on Japanese stock with GBP/JPY foreign-currency forwards.
(c) Buy quanto options on Japanese stocks.
(d) Move to Japan.

Question 27

You enter into an exchange option contract where you have the right to give up 5 shares of IBM stock in exchange for one share of Google in three months. After three months, IBM is trading at $92 per share while Google is at $430. The payoff at maturity is

A) $- 30$ .
B) Zero.
C) $+ 6$ .
D) $+ 30$ .

Question 28

You are interested in hedging a portfolio of bonds against a rise in interest rates. Which of the following approaches will be most suitable to your goal?
(a) Selling deep ITM vanilla call options and buy deep ITM vanilla put options.
(b) Selling deep OTM vanilla call options and buy deep OTM vanilla put options.
(c) Selling deep ITM cash-or-nothing calls and buy deep OTM cash-or-nothing calls.
(d) None of the above.

Question 29

You are long a portfolio of vanilla call options. Which of the following will help you hedge away your vega risk?
(a) Buying a portfolio of in-the-money vanilla put options.
(b) Buying a portfolio of out-of-the money vanilla put options.
(c) Buying a portfolio of in-the-money cash-or-nothing put options.
(d) Buying a portfolio of out-of-the money cash-or-nothing put options.

Question 30

A quanto option is sometimes called a "wrong-currency" option because the payoffs of the quanto
(a) Are in a different currency from the premium.
(b) Are computed by converting the payoffs from an underlying option in a foreign currency option back to the home currency at a pre-specified exchange rate that may be unrelated to the actual exchange rate.
(c) Are in a different currency from the investor's home currency.
(d) Are computed by converting the payoffs from an underlying home-currency option into a foreign currency at the current exchange rate.

Question 31

A stock is trading at 100. Consider a two-period binomial model in which the stock price moves up or down each period by factors $u = 1.20$ and $d = 0.80$ , respectively. The gross risk-free rate of interest per time step is 1.04. You are long a cash-or-nothing digital call option that pays $100 if $S _ { T } \geq 100$ , and nothing otherwise; and short a cash-or-nothing digital put option that pays $100 if $S _ { T } \leq 100$ , and nothing otherwise. (Here, $S _ { T }$ is the stock price at the end of two periods.) The value of your portfolio is

A) Positive.
B) zero.
C) Negative.
D) Cannot be calculated from the given information.

Question 32

You have written a put on a call, where the underlying call is written on a stock. To delta hedge yourself you can either go the underlying call or the underlying stock.
(a) short; short.
(b) short; long.
(c) long; short.
(d) long; long.

Question 33

A compound option is
(a) An option to compound the option's payoffs at a prespecified rate.
(b) An option based on compounding the price of the underlying at a prespecified rate.
(c) An option on an underlying option.
(d) An option on a compound-interest bearing investment.

Question 34

A US-based investor buys from you a quanto option in which the payoffs from a euro-denominated call on a German company are converted back into US dollars at the fixed rate of $1.25/€. To hedge this transaction
(a) You must hedge both exchange rate and equity price risk.
(b) You must hedge equity price risk but there is no exchange rate risk.
(c) You must hedge exchange rate risk but there is no equity price risk.
(d) There is nothing you need to do.

Question 35

In comparing a chooser to its straddle counterpart, which of the following statements is not valid?

A) A straddle is always worth more than chooser.
B) The delta of a straddle is always greater than that of a chooser.
C) The delta of a chooser lies between $- 1$ and $+ 1$ .
D) The delta of a straddle lies between $- 1$ and $+ 1$ .

Question 36

A chooser option gives the holder the right, on the choice date,
(a) To choose the strike price of the option.
(b) To choose the maturity date of the option.
(c) To choose whether the option is to be a call or a put.
(d) To choose whether to buy the option or take a premium refund.

Question 37

You buy an at-the-money chooser option. Immediately after you buy it, the price of the underlying increases very sharply. Other things remaining the same, the value of your chooser likely
(a) Increases.
(b) Decreases (the put now has no value).
(c) Remains constant (the increase in call value is canceled out by the decrease in put value).
(d) Goes to zero.

Question 38

Which of the following statements most accurately describes the range of possible values of the delta of a cash-or-nothing call option?

A) The delta lies between 0 and $+ 1$ .
B) The delta lies between $- 1$ and $+ 1$ .
C) The delta is $\geq 0$ .
D) The delta can take on any value, positive, negative or zero.

Question 39

Select the most accurate alternative. The theta of an in-the-money cash-or-nothing call option is
(a) Positive, as is the case for any call.
(b) Positive, because payoffs are the same once you are in-the-money and more time to maturity only increases the possibility of moving out of the money.
(c) Negative, because payoffs are the same once you are in-the-money and more time to maturity only increases the possibility of moving out of the money.
(d) Negative, as is the case for any call.

Question 40

You have written a put on a put, where the underlying put is written on a stock index. To delta hedge yourself you can either go the underlying put or the underlying index.
(a) short; short.
(b) short; long.
(c) long; short.
(d) long; long.

Question 41

Consider an at-the-money call option on the maximum of two assets. As the correlation between the two assets increases, what happens to the value of this option?
(a) It decreases.
(b) It stays the same.
(c) It increases.
(d) There is not enough information to answer this question.