Question

1. Faber Industries has a current stock price of $38 per share. A European-style call option with a strike price of $40 and four months until expiration is trading at $2.56. The risk-free rate is 6%.

1. What is the no-arbitrage value of a European-style put on Faber Industries with a strike price of $40 and 4 months until expiration? (2 points)
2. If a European-style put on Faber Industries with a strike price of $40 and 4 months until expiration is trading at $2.95, what trades are necessary to capture the available arbitrage profit? Demonstrate that the trades constitute an arbitrage by showing a positive inflow with no possibility of a loss from the transactions. (3 points)

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

2.56 + [40*(e^-0.06*4/12)] = 38 + P

2.56 + [40*(e^-0.02)] = 38 + P

2.56 + [40*0.9802(from table)] = 38 + P

Therefore, No Arbitrage Price of Put = P = 2.56 + 39.208 - 38 = $3.768

b)

Actual Price of Put < Theoretical Price. Therefore, Put is Undervalued.

Arbitrage Strategy:

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

Steps for Arbitrage:

Now,

(1) Sell (Write) Call Option at $2.56

(2) Borrow (Cost of Put + Current Spot Price - Inflow from Call) = (2.95+38-2.56) = $38.39 for 4 months @6%

(3) Buy share @ $38

(4) Buy Put Option at $2.95

Balance = 2.56+38.39-38-2.95 = 0

After 4 months,

Case 1: If Stock Price is less than $40, then Exercise Put and Lapse Call. Stock will be sold for $40 under Put contract.

Case 2: If Stock Price is greater than $40, then Exercise Call and Lapse Put. Stock will be sold for $40 under Call contract.

Case 3: If Stock Price is equal to $40, then Both Lapse. Stock will be sold for $40 in Market

Therefore, In any Case, we will be able to sell the stock for $40

(5) Sell share @ $40

(6) Repay the loan along with interest i.e. 38.39*e^0.02 = 38.39*1.0202(from table) = $39.17

Balance = Arbitrage Gain = 40 – 39.17 = $0.83