Question

You buy one Home Depot (HD) call option and one HD put option, both with a $215 strike price and a June expiration date. The call premium is $9.25 and the put premium is $23.70.

1. Your maximum loss from this position could be ________.

2. At expiration, you break even if the stock price is equal to _____.

2)

JPM stock currently sells for $90. A 6-month call option with strike price of $100 sells for $6.00, and the risk free rate is 2%.

1. According to the put-call parity, what should be the price of a 6-month put option with strike price of $100?

2. If the put option is currently priced at $17.00, state an arbitrage strategy to take advantage of this mispricing.

3. If the put option is currently priced at $13.00, state an arbitrage strategy to take advantage of this mispricing.

Answer 1

1)

a) Maximum Loss = Premium Paid for both Options = 9.25+23.7 = $32.95

b) Breakeven = Strike Price (+/-) Total Premium Paid = 215 (+/-) 32.95 = $182.05(on the lower side) and $247.95(on the upper side)

2)

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

a)

6 + [100*(e^-0.01)] = 90 + P

6 + [100*0.99(from table)] = 90 + P

6 + 99 – 90 = P

Therefore, Price of Put = P = 15

b)

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

Arbitrage Strategy:

As Put is Overvalued, Buy Call Option, Sell Stock Now, Sell Put Option and Invest

c)

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