Question

Suppose you are given the following data:

2-month option on XYZ stock:

Underlying S = 48.1

Strike X = 50

Put price = $2.2

1. What should be the price of call to prevent arbitrage if 2-month interest rate is 6% p.a.?

2. If the actual call price was $1.3 how would you implement an arbitrage opportunity?

3. Compute your payoff at maturity.

Answer 1

As per Put Call Parity, the prices of options with same strike price & expiry date are as follows:

Price of Call + PV of Exercise Price = Spot Price (Current Stock Price) + Price of Put

Interest Rate is assumed as continuous compounding

C + [50*(e^-0.06*2/12)] = 48.1 + 2.2

C + [50*(e^-0.01)] = 50.3

C + [50*0.99(from table)] = 50.3

Therefore, Price of Call for NO ARBITRAGE = C = 50.3 – 49.5 = $0.8

Actual Price of Call > Theoretical Price. Therefore, Call is Overvalued.

Arbitrage Strategy:

As Call is Overvalued, Sell Call Option, Borrow, Buy Stocks Now and Buy Put Option

Payoff at Maturity = Strike Price - [(Cost of Put + Current Spot Price - Inflow from Call)*e^0.01]

Arbitrage Strategy is such that, in ANY case, we will be able to sell the share at Strike Price. Amount Borrowed will be equal to (Cost of Put + Current Spot Price - Inflow from Call). There will be No Cash Flow at the Beginning. After 2-months, Cash Inflow will be Strike Price - Loan Payable alongwith Interest.

Therefore, Payoff = 50 - [(2.2+48.1-1.3)*e^0.01] = 50 - [48.9*1.0101] = 50 - 49.39389 = $0.60611 per share