Exotic Option Payoffs: Barrier and Asian

(a) A down-and-out call has strike $K = 100$ and barrier $H = 90$. The stock starts at $S_0 = 105$. If the stock ever touches 90 before expiry, the option ceases to exist (knocks out). Explain qualitatively: is this option cheaper or more expensive than a vanilla call? By roughly how much? (b) An Asian call pays $\max\left(\frac{1}{T}\int_0^T S_t \, dt - K, \, 0\right)$. The payoff depends on the average price rather than the terminal price. Is this option cheaper or more expensive than a vanilla call? Why? (c) You hold a down-and-out call and the stock is at 91 (one dollar above the barrier). Is your delta higher or lower than a vanilla call's delta? Why?