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**

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