Question

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?

Answer 1

Steps for given Arbitrage Strategy:

Today,

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

2) Buy Stock for $100

3) Buy Put for $8

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