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)
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 |
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