Question

Suppose that a financial institution has sold for $300,000 a European call option on 100,000 shares of a non-dividend stock. Assume that the stock price is $49, the strike price is $50, the risk-free interest rate is 5% per annum, the stock price volatility is 20% per annum, the time to maturity is 20 weeks (0.3826 years), and the expected return from the stock is 13% per annum.

(b) (Strategy 1) The financial institution decides to do nothing but deposit $300,000 in a risk-free bank. Then calculate the profit (or cost) of the financial institution at maturity in case when after 20 weeks (i) the stock price is $40 or (ii) the stock price is $60.

Answer 1

Particulars	(I) If stock price at maturity is $40	(II) If stock price at maturity is $60
Note-Selling call option means taking an obligation to sell the share at the maturity if the Buyer of the option, exercises the option at maturity.For selling the call option the financial institution will receive the option premium
Option premium received due to selling of the call option and deposited it in risk free bank	300000	300000
Amount to be received after 20 weeks from the deposit	305739	305739
$300000+[$300000*5%*0.3826 year]
Price at maturity	40	60
Strike price	50	50
Will buyer exercise the option	No	Yes
	[because the buyer can buy the share @40 from the market instead of buying it @50]	[because buyer will buy the shaer@50 as per the option contrcat and can sell it@60 at market
Net profit/(cost)	305739	-694261
		[(50-60)*100000]+305739
		Explanation-The Financial institution will buy the share from the market@60 and sell it to the buyer of the option@50 as per the option contract.