Question

Consider a call and a put on a non dividend paying stock; both for T = 1yr. The stock price is $45/share and K = $45/share for both options. The Call premium is equal to the put premium c = p = $7/share. The annual risk-free rate is 10%.

7.1 Use the put-call parity and show that there exists an arbitrage opportunity.

7.2 Show the complete table of cash flows and P/L at the options expiration of a strategy that will create the arbitrage profit in 2.1.

Answer 1

Stock PRICE = $45

Strike price = $45

call premium = put premium = $7

Risk free rate = 10%

Put call parity equation :

Call premium + Strike price / (1+ risk free rate ) ^n = Stock price + Put price

So

7 + 45 / 1.1 = 7 + 45

47.91 = 52

Since both the sides are not equal, there is an arbitrage opportunity

7.2

Since right side of the equation is costly than the left side, we will :

Short sell share

Sell Put

Buy zero coupon bond with 10% and 1 year

Buy call option

So

1. Short sell share, you will get cash of = 45

2. Sell put, you will get premium = 7

Total cash inflow = 52

3. Buy bond, you have to pay present value = 45 / 1.1 = 40.91

Buy call option, you need to pay = 7

Total cash outflow = 47.91

So net cash flow = 52 - 47.91 = 4.1

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