Question

A one-year call option has a strike price of 60, expires in 6 months, and has a price of $2.5. If the risk-free rate is 7 percent, and the current stock price is $55, what should the corresponding put be worth?

a. $5.00

b. $7.54

c. $7.08

d. $5.50

Answer 1

Given,

Strike price = $60

Maturity(n) = 6 months or 0.5 year

Call price = $2.5

Risk free rate (r) = 7% or 0.07

Current stock price = $55

Solution :-

Put = Call price - Current stock price + [strike price (1 + r)ⁿ]

= $2.5 - $55 + [$60 (1 + 0.07)^0.5]

= $2.5 - $55 + [$60 (1.07)^0.5]

= $2.5 - $55 + [$60 1.03440804]

= $2.5 - $55 + $58 = $5.50

Thus, the corresponding put should be worth $5.50