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 (C_{0})

Strike Price = $ 28. (X)

Maturity = 6 months (n)

European put Price = $ 3 (P_{0})

Stock Price today (ex-dividend) = $ 28 - (1 /
e^{0.06*4/12}) = $ 27.02 (S_{0})

Now, as per Put-Call Parity theory,

P_{0} + S_{0} = C_{0} + PV of X

Let us find theoretical price of put using this theory,

P_{0} (Theoretical) + 27.02 = 2 + 28 /
e^{0.06*6/12}

So, P_{0} (Theoretical) = $ 2.15

P_{0} (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)*

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