In the given example, I dont think it is possible. Look at the following computations ignoring time value of money
Buy shares at 200. Sell call option for 30. You are now minus 170. If share price goes below 180 the call option get exercised. Between 170 and 180 there is a possibility of loss, but if the price goes below 170, we lose creating no arbitrage.
Second way is short sell shares and buy a call option. We are now positive 170 (cash in hand). If the price goes below 170, we will buy from the market and deliver making a profit. But if it goes above 170 we make a loss. If it goes above 180, we can exercise the option, but still we lose.
Even if we put time value of money the answer will be the same. Theoretical min price is not relevant as we dont know whether the option market price will move in that direction or not. Otherwise we could have simply bought the option and sold it later.
Are you sure you got all info necessary to solve this question. Pls revert.
20 October 2010
i have provided all the details as given in the qstn...
following is the answer suggstd in d book...
We short sell d given stock as on today at Rs. 200 As on today we buy a call option for Rs. 30.
Invest the net amount 200-30 = Rs. 170.
Now if d market price on expiry is lower(let us say Rs. 175) we will not exercise d option and will buy the stock from market itself at Rs. 175. And amnt recvd on investd money(Rs.170) cc@10% will come out to be Rs. 187 on expiry.
and finally the riskless profit is equal to 187-175 = Rs.12.
same way the case if market price is higher is discussed in the book.
ISSUE : while calculating the riskless profit why isnt the option premium paid earlier i.e. Rs. 30 considered??
My View : there isnt prfoit infact there is net loss dis way cz OP of Rs. 30 should also be given a consideration n accordingly loss will be 12-30 = Rs.18
20 October 2010
Max arbitrage profit is Rs. 7 which is 187 recd from deposit minus 180 strike price.
To answer your query, you should look at it from a cash flow point of view.
Short sell and buy option - Net cash inflow is 170 Deposit this cash - Net cash outflow is 170. Now cash in hand is zero. On the strike Day: Price below 180 then buy from market. Out flow is 180 or less. Inflow is 187. Net in hand is 7 or more Price above 180 then exercise the option. Outflow is 180 exactly. Inflow is 187. Net in hand is 7.
20 October 2010
Why I went wrong? In practice you cannot short sell and wait for one year to deliver the shares. You have delivery depending on market settlement which is less than a week. This is why I decided to ignore 10% in the question. Some exam questions do ignore practical aspects.
If you still havent understood please revert, I will try another method to explain.
CAclubindia
