Hi, Could u help to solve these quant questions?

1. Consider the Black-Scholes stock process dSt = rStat + oStdWt where We is a standard Brownian motion under the risk-neutral measure Q* associated with the risk-free bond numeraire. A European contract pays Vr = log ST on maturity date T. (a) Derive the valuation formula for this contract. (b) Derive the delta () and (T) of this contract. 2. Derive the valuation formula for a cash-or-nothing digital call option struck at K and maturing at T Vr = 1ST >K under the Black-Scholes model. Proceed to derive its (a) delta (b) vega 3. Consider a portfolio II consisting of an option V and A amount of stock S, i.e. IIt = Vt + A x St. The stock pays no dividend and its price follows the lognormal stochastic differential equation dSt = uStat + oSidWt. (a) Use Ito's formula to write down the SDE for the process dVt. (b) Write down the process dlIt, and determine what choice of A will give rise to a risk-free portfolio. (c) A risk-free portfolio must earn the continuously compounded risk-free rate by no-arbitrage. Show that this leads to the Black-Scholes partial differential equation