Question

Based on the put-call parity relationship you want to make an arbitrage profit by selling a...

Based on the put-call parity relationship you want to make an arbitrage profit by selling a call, buying a put, and taking a leveraged equity position.

Stock proce = \$100
Call price (6-month maturity with strike price of \$110) = \$5
Put price (6-month maturity with strike price of \$110) = \$8
Risk free interest rate (continuously compounded) = 10%

If the stock price at maturity is \$120, how much do you earn from all these positions?

Steps for given Arbitrage Strategy:

Today,

1) Borrow Amount (Stock Price+Put Premium-Call Premium) = 100+8-5 = \$103 for 6 months @10%

4) Sell Call for \$5

Balance = 103-100-8+5 = 0

After 6 months,

Case 1: If Stock Price is less than \$110, then Exercise Put and Lapse Call. Stock will be sold for \$110 under Put contract.

Case 2: If Stock Price is greater than \$110, then Exercise Call and Lapse Put. Stock will be sold for \$110 under Call contract.

Case 3: If Stock Price is equal to \$110, then Both Lapse. Stock will be sold for \$110 in Market

Therefore, In any Case, we will be able to sell the stock for \$110

5) Sell Stock under Call contract for \$110

6) Repay loan with interest = 103*e^(0.1/2) = 103*e^0.05 = 103*1.0513(from table) = \$108.28

Balance = Arbitrage Gain = 110-108.28 = \$1.72

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