Question

The premium of a call option with a strike price of $45 is equal to $5 and the premium of a call option with a strike price of $50 is equal to $3.5. The premium of a put option with a strike price of $45 is equal to $3. All these options have a time to maturity of 3 months. The risk-free rate of interest is 8%. In the absence of arbitrage opportunities, what should be the premium of a put option with a strike price of $50?

Answer 1

First of all lets find Spot price

According to put call parity

C+ PV(x) = P + S

S = spot price

P = Put premium = 3 $

C = Call premium = 5 $

PV(x) = Present value of strike price = 45 x(1/(1+r))^n

r = rate of interest = 8%

n = 3 months

thus Present value of strike price = 45 x (1/(1+8%)^3/12

=45 x (1/(1.08))^0.25

= 45 x 0.9894

= 44.1425

Thus , C+ PV(x) = P + S

= 5 + 44.1425 = 3 +S

S = 46.1425 $

Now we shall find premium of put option with strike price 50$

According to put call parity

C+ PV(x) = P + S

S = spot price

P = Put premium = ?

C = Call premium = 3.5 $

Present value of strike price = 50 x (1/(1+8%)^3/12

=50 x (1/(1.08))^0.25

= 50 x 0.9894

= 49.0472 $

Thus C+ PV(x) = P + S

= 3.5 + 49.0472 = P + 46.1425

=52.5472 = P + 46.1425

P = 6.4047 $