A stock is trading today at $80 a share. Next year, it will trade at either $100 or $64. A European call option is trading on this stock with the strike price of $90 and one year to expiration. The risk-free rate of interest is 5% per year.

a)Find the delta of the call. Is it positive or negative?

b)Explain in a short paragraph why delta of a call option has this sign.

c)Suppose you purchase 2777.78 shares of stock and write 100 call contracts. Show that the value of this portfolio in one yearwill be the same regardless of the stock price. You may use the last two columns of the following table:

	Today	In one year
		St = 100	St = 64
Value of 2777.78 shares
Value of 100 call contracts
Total value

d)Since the portfolio of 2777.78 shares and 100 short call contracts has the same value regardless of the stock price, it is essentially risk-free. Therefore, it must earn the risk-free rate of return. Using this fact, what must be the total value of the portfolio today?

e)What is the call premium today?