Let D, be the price of the digital Call option at time t with payoff function at maturity T: H if ST > K 0 if ST < K, DT = where H and K are constants. The dynamic of the underlying asset in the risk neutral world is given by dSt (rq)Stdt + o StdWt, = where r is the (constant) risk-free rate, q is the (constant) dividend rate per unit of time, o is the (constant) volatility of the underlying, W, is a Brownian motion on the risk neutral probability space (N, F, P). i) Using Ito's formula, find the asset price ST in terms of the current price St. ii) Using the risk neutral valuation, find the price Dt of the digital option