(b) The Black Scholes formula for a European Vanilla Put option P is given by P(S,t)=Eer(Tt)N(d2)SN(d1) where N is the cumulative distribution function for a standardized normal random variable given by N(x)=21xey2/2dyd1=Ttlog(S/E)+(r+2/2)(Tt) and d2=Ttlog(S/E)+(r2/2)(Tt). In the above S is the underlying, t is time, E is the exercise price, T is the expiry date, r is the risk-free interest rate and is the volatility. (i) Show that the above expression for P(S,t) satisfies the Payoff function for a Vanilla Put option at time t=T. (ii) Determine an expression for the Delta of a Vanilla Put option where =P/S