Question

One stock is selling for $54 per share. Calls and puts with a $55 strike and 360 days until expiration are selling for $8 and $4, respectively. What is the arbitrage profit, if we trade on one call and one put? Suppose risk-free rate is 10%.

Answer 1

As per the put-call parity equation, C + (K/(1 + r)t) = P + S,

where C = price of call option,

P = price of put option,

S = current stock price

K = strike price of option

r = risk free rate

t = time to expiration in years

We plug in the values into the equation :

C + (K/(1 + r)t) = P + S

8 + (50/(1 + 10%)1) = 4 + 54

8 + 50 = 4 + 54

58 = 588

We can see that the left hand side equals the right hand side

Therefore, there is no arbitrage opportunity. Arbitrage profit = $0

Answer 2