Question

A call option of non-divided paying stock is traded at price of $5. The current spot price of this stock is $50. The call has a six-month maturity and a strike price of $52. The risk-free rate of return is 3.9%. What would be the price of a put on the same stock, maturity and strike price that of the call?

5

6

4

3

Answer 1

Given

Price of an European call option = $ 5

Spot price of a stock = $ 50

Strike price = $ 52

Rate of return = 3.9%

We know that

According to put Call parity theorem C+ PV ( X) = P+S

Here C = Price of Call option

PV ( X) = Present value of strike price

P = Price of a Put option

S = Spot price

Computation of Present value of strike price.

We know that Present value = Future Value / ( 1+i)^n

Here I = Rate of interest

n = No.of Years

Present value = $ 52 / ( 1+0.039)^0.5

= $ 52/( 1.039)^0.5

= $ 52/1.019313

= $ 51.0148

According to put Call parity theorem C+ PV ( X) = P+S

$ 5+$ 51.0148=P+$ 50

$ 51.0148-$ 50= P-$5

$ 1.0148=P-$ 5

$ 1.0148+$ 5 = P

$ 6.0148 =P

Hence the Price of an put option is approximately$ 6. So option 2 is the Correct answer.