Question

Assume put-call parity holds. One stock is selling for $33 per share. Calls with a $30 strike and 180 days until expiration are selling for $6. What should be the put price? Suppose risk-free rate is 4%.

Answer 1

As per Put Call Parity, the prices of options with same strike price && expiry date are as follows:

Price of Call + PV of Exercise Price = Spot Price (Current Stock Price) + Price of Put

Interest Rate is assumed as continuous compounding

Interest Rate for 180 days = 0.04/2 = 0.02

6 + [30*(e^-0.02)] = 33 + P

6 + [30*0.9802(from table)] = 33 + P

6 + 29.406 – 20.45 = P

Therefore, Price of Put = P = 14.956

Answer 2

As per put call parity

Call price + PV of exercise price = Spot price + Put price

6+30*e^(-0.04*0.5)=33+Put value

Put value = 2.406