Consider European call and pit 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%. Use the put-call parity and show that there exist an arbitrage opportunity. Also, show the complete table of cash flows and P/L at the options expiration of a strategy that will create the arbitrage profit in Q2.
SOLUTION:-
Use the put-call parity and show that there exists an arbitrage opportunity.
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
Show the complete table of cash flows and P/L at the options expiration of a strategy that will create the arbitrage profit in Q2.
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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