Question 1

When dividends increase with all else remaining the same,which of the following is true?

Accepted Answer

Dividends during the life of an option reduce the final stock price.As a result dividend increases cause puts to increase in value and calls to decrease in value.

Question 2

When volatility increases with all else remaining the same,which of the following is true?

Accepted Answer

Volatility increases the likelihood of a high payoff from either a call or a put option.The payoff can never be negative.It follows that as volatility increases the value of all options increase.

Question 3

Which of the following is NOT true? (Present values are calculated from the end of the life of the option to the beginning.)

Accepted Answer

If it is optimal to exercise an American option today and the stock price is very low the option will be worth more than the present value of the strike price

Question 4

A stock price (which pays no dividends)is $50 and the strike price of a two year European put option is $54.The risk-free rate is 3% (continuously compounded).Which of the following is a lower bound for the option such that there are arbitrage opportunities if the price is below the lower bound and no arbitrage opportunities if it is above the lower bound?

Accepted Answer

The lower bound in Ke^-rT −S₀ In this case it is 54e^−0.03×2 - 50= $0.86.

Question 5

Which of the following describes a situation where an American put option on a stock becomes more likely to be exercised early?

Accepted Answer

As the volatility of the option decreases the time value declines and the option becomes more likely to be exercised early.In the case of A and B,time value increases and the option is less likely to be exercised early.

Question 6

The price of a stock,which pays no dividends,is $30 and the strike price of a one year European call option on the stock is $25.The risk-free rate is 4% (continuously compounded).Which of the following is a lower bound for the option such that there are arbitrage opportunities if the price is below the lower bound and no arbitrage opportunities if it is above the lower bound?

Accepted Answer

The lower bound in S₀− Ke^-rT.In this case it is 30 - 25e^-0.04×1= $5.98.

Question 7

A European call and a European put on a stock have the same strike price and time to maturity.At 10:00am on a certain day,the price of the call is $3 and the price of the put is $4.At 10:01am news reaches the market that has no effect on the stock price or interest rates,but increases volatilities.As a result the price of the call changes to $4.50.Which of the following is correct?

Accepted Answer

The price of the call has increased by $1.50.From put-call parity the price of the put must increase by the same amount.Hence the put price will become 4.00 +1.50 = $5.50.

Question 8

The price of a European call option on a non-dividend-paying stock with a strike price of $50 is $6.The stock price is $51,the continuously compounded risk-free rate (all maturities)is 6% and the time to maturity is one year.What is the price of a one-year European put option on the stock with a strike price of $50?

Accepted Answer

Put-call parity is c+Ke^-^rT=p+S₀.In this case K=50,S₀=51,r=0.06,T=1,and c=6.It follows that p=6+50e^-0.06×1−51 = 2.09.

Question 9

Which of the following is true?

Accepted Answer

An American call option should never be exercised early when the underlying stock does not pay dividends.There are two reasons.First,it is best to delay paying the strike price.Second the insurance provided by the option (that the stock price will fall below the strike price)is lost.

Question 10

The price of a European call option on a stock with a strike price of $50 is $6.The stock price is $51,the continuously compounded risk-free rate (all maturities)is 6% and the time to maturity is one year.A dividend of $1 is expected in six months.What is the price of a one-year European put option on the stock with a strike price of $50?

Accepted Answer

Put-call parity is c+Ke^-rT=p+S₀˗D.In this case K=50,S₀=51,r=0.06,T=1,and c=6.The present value of the dividend,D,is 1×e^−0.06×0.5 = 0.97.It follows that p=6+50e^-0.06×1−(51-0.97)= 3.06.

Question 11

Which of the following is true when dividends are expected?

Accepted Answer

Put call parity still holds for European options providing the present value of the dividends is subtracted from the stock price.

Question 12

When the strike price increases with all else remaining the same,which of the following is true?

Accepted Answer

Strike price increases cause the values of puts to increase and the values of calls to decline.

Question 13

Interest rates are zero.A European call with a strike price of $50 and a maturity of one year is worth $6.A European put with a strike price of $50 and a maturity of one year is worth $7.The current stock price is $49.Which of the following is true?

Accepted Answer

In this case because interest rates are zero c+K=p+S₀.The left side of this equation is 50+6=56.The right side is 49+7=56.There is no mispricing.

Question 14

Which of the following is the put-call parity result for a non-dividend-paying stock?

Accepted Answer

The put-call parity result is c+Ke^-rT=p+S₀.

Question 15

When the stock price increases with all else remaining the same,which of the following is true?

Accepted Answer

Stock price increases cause the values of calls to increase and the values of puts to decline.

Question 16

When the time to maturity increases with all else remaining the same,which of the following is true?

Accepted Answer

When the time to maturity increases from X to Y,European options usually increase in value.But this is not always the case.For example,European call options can decrease in value if a big dividend is expected between X and Y.

Question 17

Which of the following best describes the intrinsic value of an option?

Accepted Answer

The intrinsic value of an option is the value it would have if it were about the expire which is the same as the value in A.

Question 18

Which of the following can be used to create a long position in a European put option on a stock?

Accepted Answer

As payoff diagrams show a call on a stock combined with a short position in the stock gives a payoff similar to a put option.Alternatively we can use put-call parity,which shows that a call minus the stock equals the put minus the present value of the strike price.

Question 19

Which of the following is true for American options?

Accepted Answer

Put call parity provides both an upper and a lower bound for the difference between call and put prices.See equation (11.11).

Question 20

When interest rates increase with all else remaining the same,which of the following is true?

Accepted Answer

Calls increase and puts decrease in value.As explained in the text an increase in interest rates causes the growth rate of the stock price to increase and the discount rate to increase.An increase in interest rates therefore reduces the value of puts because puts are hurt by both a discount rate increase and a growth rate increase.For calls it turns out that the growth rate increase is more important than the discount rate increase so that their values increase when interest rates increase.(Note that we are assuming all else equal and so the asset price does not change.)

Quiz 11: Properties of Stock Options