Question

# The price of a European call that expires in six months and has a strike price...

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?

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 / e0.06*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 / e0.06*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)

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