Question

The price of a European call that expires in six months and has a strike price of $28 is $2. The underlying stock price is $28, and a dividend of $1 is expected in 4 months. The term structure is flat, with all risk-free interest rates being 6%. If the price of a European put option with the same maturity and strike price is $3, what will be the arbitrage profit at the maturity?

Answer 1

European Call Price = $ 2 (C₀)

Strike Price = $ 28. (X)

Maturity = 6 months (n)

European put Price = $ 3 (P₀)

Stock Price today (ex-dividend) = $ 28 - (1 / e^0.06*4/12) = $ 27.02 (S₀)

Now, as per Put-Call Parity theory,

P₀ + S₀ = C₀ + PV of X

Let us find theoretical price of put using this theory,

P₀ (Theoretical) + 27.02 = 2 + 28 / e^0.06*6/12

So, P₀ (Theoretical) = $ 2.15

P₀ (Actual) = $ 3.

Hence, there is mis-pricing and thus scope for arbitrage.

Arbitrage Profit = Mis-pricing = $ 3 - $ 2.15 = $ 0.85 per option.

(Note : We can also calculate theoretical price of call option and compare with actual call price, it will yield the same arbitrage profit of $ 0.85 per option)