A digital call is an option that pays 0 below the strike price and one 1 above the strike price. A digital put is an option that pays 0 above the strike price and one 1 below the strike price. Derive the expression for the price of an at-the-money digital call given that (i) the price of an at-the-money digital put is ert N(-d2), (ii) N(x)+N(-x) = 1, and (iii) the present value of a dollar is exp(-rt). Provide a brief explanation for key steps/assumptions in your derivation.