Question

Consider a European call and a European put on a non-dividend-paying stock. Both the call and the put will expire in one year and have the same strike prices of $120. The stock currently sells for $115. The risk-free rate is 5% per annum. The price of the call is $7 and the price of the put is $5. Is there an arbitrage? If so, show an arbitrage strategy. (To show the arbitrage, present the table listing actions and resulting cash flows)

Answer 1

Solution:

It is given that call premium C = $7

Put premium P = $5

Spot rate S = $115

Strike price X = $120

Interest rate = 5%

Time period = 1 year

We will use put call parity formula to check the arbitrage opportunity

C + X * exp ( - interest rate * time ) = P +S

7 + 120 * exp ( -5% * 1 ) = $5 + $115

7 + 120 *0.951229 = $5 + $115

7+ 114.1475 = 120

121.1475 = 120

Since both sides are not equal hence there exists an arbitrage opportunity and arbitrage profit will be the difference = 121.1475 - 120 = 1.1475.

In order to exploit the arbitrage profit we need to sell higher side and buy lower side

Strategy and cash flow

Strategy	cash flow
Sell a call option and earn premium	+7
Sell a bond of value 114.1475	+114.1475
Buy a put option and pay premium	-5
Buy a stock	-115
Net	1.1475