Question

Assume that the price of a European call expiring in six-month with a strike price of $30 is $2. Suppose that the underlying stock price is $29, and a dividend of $0.50 is expected in two months and again in 5 months. The interest rate is the same for all periods and the risk-free rate is 10%. The price of a European put option that expires in six-month and has a strike price of $30 is:
a. $1.51
b. - 2.51
c. $2.51
d. $3.05

Answer 1

Answer:

correct option is c. $2.51

Explanation:

given data

strike price of $30 = $2

underlying stock price = $29

dividend = $0.50

risk-free rate = 10%

solution

we use here pit call parity  that is

c - p = s - k $e^{-rt}$ -D    .....................1

S is current price and c is call premium and r is rate and t is time

so price of put p will be

p = c-s + k $e^{-rt}$ + D

put here value and we get

p  = 2 -29 + 30  $e^{-0.1*0.5}$ + 0.5  $e^{-0.1*2/12}$  + 0.5 $e^{-0.1*5/12}$

p  = 2.508

p = $2.51

so correct option is c. $2.51