Chapter 10 Properties of Stock Options

15) 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?

A) $9.91

B) $7.00

C) $6.00

D) $2.09

16) 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?

A) $8.97

B) $6.97

C) $3.06

D) $1.12

17) 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?

A) The put price increases to $6.00

B) The put price decreases to $2.00

C) The put price increases to $5.50

D) It is possible that there is no effect on the price

18) 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?

A) The call price is high relative to the put price

B) The put price is high relative to the call price

C) Both the call and put must be mispriced

D) None of the above

19) Which of the following is true for American options?

A) Put-call parity provides an upper and lower bound for the difference between call and put prices

B) Put call parity provides an upper bound but no lower bound for the difference between call and put prices

C) Put call parity provides an lower bound but no upper bound for the difference between call and put prices

D) There are no put-call parity results

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

A) Buy a call option on the stock and buy the stock

B) Buy a call on the stock and short the stock

C) Sell a call option on the stock and buy the stock

D) Sell a call option on the stock and sell the stock