Question

Consider a European call option and a European put option, both of which have a strike price of $70, and expire in 4 years. The current price of the stock is $60. If the call option currently sells for $0.15 more than the put option, the continuously compounded interest rate is

a. 2.9%         

b. 3.9%

c. 4.9%

d. 5.9%

       

Answer 1

it is given call option(c) sells $0.15 more than put option(p)

so we can say that c - p = 0.15

as per put call parity

call premium(c) + Present value of the strike(X*e^-rT) = Put premium(p) + current price(S)

re write the above equation

c - p = s - X*e^-rT

X = strike price

r = continuous rate of return

T = time period

0.15 = 60 - 70*e^-rT

let rT = x

e^-x = (60 - 0.15) / 70

e^-x = 0.855

e^x = 1/0.855

we know value of e = 2.718282

2.718282^x = 1.16959

applying log on both sides

x log(2.718282) = log(1.16959)

x = log(1.16959) / log(2.718282)

x = 0.1566

x = r*T

we know T = 4 years

r*4 = 0.156654

r = 0.156654 / 4

r = 0.039 or 3.9%

Option b is correct.