Deck 10: Properties of Stock Options

Question 1

Which of the following are always positively related to the price of a European call option on a stock? choose three)

A) The stock price
B) The strike price
C) The time to expiration
D) The volatility
E) The risk-free rate
F) The magnitude of dividends anticipated during the life of the option

Answer 1

A), D, AND E

Question 2

What to the nearest cent) is the lower bound for the price of a six-month European put option on a stock when the stock price is $40, the strike price is $46 and the risk-free interest rate with continuous compounding is 6% per annum? _ _ _ _ _ _

Answer 2

$4.64

Question 3

A call and a 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. What would you expect the price of the put to change to? _ _ _ _ _ _

Answer 3

$5.50.

Question 4

What is the answer to question 2 if the option is American? _ _ _ _ _ _

Question 5

What is the answer to question 4 if the option is American? _ _ _ _ _ _

Question 6

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% per annum, and the time to maturity is one year. What to the nearest cent) is the price of a one-year European put option on the stock with a strike price of $50? _ _ _ _ _ _

Question 7

What is the answer to question 6 if a dividend of $1 is expected in six months? _ _ _ _ _ _

Question 8

What to the nearest cent) is the lower bound for the price of a two-year European call option on a stock when the stock price is $20, the strike price is $15, and the risk-free interest rate with continuous compounding is 5% per annum and there are no dividends? _ _ _ _ _ _