Deck 16: Option Relations

Question 1

Suppose p is the current price of a European put and p_A is that for an American put,where the two options have identical terms and conditions and differ only in terms of the early exercise feature.If B = $0.96 is today's price of a zero-coupon bond that matures on the option's expiration date and K = $50 is the strike price,then the following statement is correct:

A) p $\le$ $50 and p_A $\le$ 48
B) p $\ge$ $24 and p_A $\le$ 25
C) p $\le$ $48 and p_A $\le$ 50
D) p $\le$ $48 and p_A $\ge$ 48
E) None of these answers are correct.

Answer 1

p $\le$ $48 and p_A $\le$ 50

Question 2

The current price of YBM stock S is $101.European options with a strike price K = $100 and maturing in T = 6 months trade on YBM.The continuously compounded,risk-free interest rate r is 5 percent per year.If the call price c is $7.50 and the put price p is $4.60,then the arbitrage profits that you can make today by trading one contract of each option (one contract is based on 100 shares)are:

A) 0
B) $57
C) $112
D) $198
E) None of these answers are correct.

Answer 2

$57

Question 3

It may make sense to exercise early an American call option (like the ones that trade in the Chicago Board Options Exchange)just before the time of:

A) a stock dividend payment
B) a stock split
C) a reverse stock split
D) a cash dividend payment
E) None of these answers are correct.

Answer 3

D

Question 4

Suppose c and p are the current prices of a European call and put,while c_A and p_A are those corresponding to American options.If today's price of the stock underlying the options is S,a zero-coupon bond that matures on the common expiration date for the options is B,and the common strike price is K,then the following statement is INCORRECT:

A) c $\ge$ max(S - BK,0)
B) c_A $\ge$ max(S - BK,0)
C) c $\ge$ max(BK - S,0)
D) p $\ge$ max(BK - S,0)
E) p_A $\ge$ max(K - S,0)

Question 5

The current price of YBM stock S is $101.European options with a strike price K = $100 and maturing in T = 6 months trade on YBM.The continuously compounded,risk-free interest rate r is 5 percent per year.A dividend of $1.10 is paid out after three months.If the put price p is $4.03,the call price c is:

A) $5.25
B) $6.41
C) $7
D) $7.49
E) None of these answers are correct.

Question 6

The current price of YBM stock S is $101.European options with a strike price K = $100 and maturing in T = 6 months trade on YBM.The continuously compounded,risk-free interest rate r is 5 percent per year.If the call price c is $7.50,the put price p is:

A) $4.03
B) $5.03
C) $5.60
D) $6.75
E) None of these answers are correct.

Question 7

Consider options that are identical in all respects except for the differences that are mentioned.Then which of the following statements is INCORRECT?

A) The difference in American call prices cannot exceed the difference in exercise prices.
B) The price difference between two European puts cannot exceed the difference in exercise prices.
C) The longer the time until expiration,the less valuable an American put is.
D) Before expiration,an American put must be worth at least the exercise price less the stock price.
E) Before expiration,a call option must be worth at least the stock price less the present value of the strike price.

Question 8

A cash dividend lowers the value of:

A) a cash-protected American call
B) a cash-protected American put
C) an exchange-traded American call
D) an exchange-traded American put
E) an exchange-traded European put

Question 9

The current value of INDY index is 1,015 and a portfolio replicating this index has a value of $1,015.European options with a strike price K = $1,000 and maturing in T = 6 months trade on YBM.The continuously compounded,risk-free interest rate r is 5 percent per year.The stocks underlying INDY index have a dividend yield $\delta$ = 1.2 percent per year.A trader quotes a call price c= $80 and a put price p = $37.Then,the amount of arbitrage profits that you can make by trading securities based on one share of INDY are:

A) 0
B) $3.31
C) $6.07
D) $9.38
E) None of these answers are correct.

Question 10

Consider a stock that pays no dividends whose value equals the strike price of a call and put with identical contract terms on the stock.Interest rates are positive.Then,which of the following is true?

A) the call price must equal the put price
B) the call price will be greater than the put price
C) the call price will be less than the put price
D) the call price will be less than or equal to the put price
E) None of these answers are correct.

Question 11

Consider a call and a put written on a stock that pays no dividends.If the interest rate is positive and the options have the same price and identical contract terms,then which of the following is true?

A) stock price = strike price
B) stock price is greater than the strike price
C) stock price is greater than or equal to the strike price
D) stock price is less than the strike price
E) need more information

Question 12

Consider options that are identical in all respects except for the differences that are mentioned.Then which of the following statements is INCORRECT?

A) Exercise an American call the first time its price is equal to the stock price minus the strike price.
B) Exercise an American put the first time its price is equal to the strike price minus the stock price.
C) Exercise an American put early when the stock price is small enough relative to the strike price with consideration for the time to maturity.
D) Never exercise early an American call on a stock that pays no dividends over the option's life.
E) The only times when it may be optimal to exercise early an American call would be just after the stock goes ex-dividend.

Question 13

The current price of YBM stock S is $101.European options with a strike price K = $100 and maturing in T = 6 months trade on YBM.If the call price c is $8.07 and the put price p is $3.63,then the annual continuously compounded risk-free interest rate r is:

A) 4.55 percent
B) 6 percent
C) 6.65 percent
D) 7 percent
E) None of these answers are correct.

Question 14

Consider options that are otherwise identical.Then,the following statement is INCORRECT:

A) the longer the time until expiration,the greater the price of a European put
B) the lower the strike price,the more valuable the European call
C) the higher the strike price,the more valuable the European put
D) the longer the time until expiration,the greater the price of an American call
E) the longer the time until expiration,the greater the price of a European call

Question 15

The current price of YBM stock S is $101.European options with a strike price K = $100 and maturing in T = 6 months trade on YBM.The continuously compounded,risk-free interest rate r is 5 percent per year.If the put price p is $2.70,then the call price c is:

A) $4.03
B) $5.17
C) $6.17
D) $8.03
E) None of these answers are correct.

Question 16

In the absence of cash dividends,you may exercise the following option early:

A) an American put option
B) an American call option
C) a European put option
D) a European call option
E) None of these answers are correct.

Question 17

The following is NOT an example of tax or regulatory arbitrage:

A) STRIPS (Separate Trading of Registered Interests and Principal of Securities)program of the US Treasury
B) Russell Sage using put-call parity to go around New York's usury laws that set a maximum amount that a lender could charge borrowers
C) using an equity swap to invest in a security market where some investors (such as foreigners)are prohibited from investing
D) creation of Eurodollars to overcome Regulation Q,which put a ceiling on the maximum interest rate that US banks could pay their depositors
E) using a currency swap or an equity swap to invest in a security market where some investors (such as foreigners)are prohibited from investing

Question 18

The following can be incorporated into an adjusted put-call parity (still an equality)for European options:

A) known dividends
B) short-selling restrictions
C) transactions costs (such as brokerage commissions,bid and ask prices,and price impact of trades)
D) taxes
E) lack of perfectly divisibility of assets

Question 19

Which of the following statements is INCORRECT?

A) American and European calls on a non-dividend stock always have the same value.
B) American and European puts on a non-dividend stock always have the same value.
C) An American put may be exercised early when the stock gets close enough to zero.
D) An American put is more likely to be exercised after the stock goes ex-dividend,rather than before the stock goes ex-dividend.
E) An American call is more likely to be exercised before the stock goes ex-dividend,rather than after the stock goes ex-dividend.

Question 20

The current price of YBM stock S is $101.American options with a strike price K = $100 and maturing in T= 6 months trade on YBM.The continuously compounded,risk-free interest rate r is 5 percent per year.If the American put price p_A is $2.70,then the American call price c_A will attain or lie between:

A) $3.70 and $6.17
B) $6.50 and $7.50
C) $7 and $7.50
D) $6 and $8.83
E) None of these answers are correct.

Question 21

Given strictly positive interest rates and an underlying stock that pays no dividends,the best way to close out a long American call option position early is to:

A) exercise the call
B) sell the call
C) buy the call
D) exchange for a physical
E) None of these answers are correct.