put–call parity relationship

1. Is a European down-and-out option on an asset worth the same as a European downand-out option on the asset’s futures price for a futures contract maturing at the same time as the option?
2. Answer the following questions about compound options:
(a) What put–call parity relationship exists between the price of a European call on a call and a European put on a call? Show that the formulas given in the text satisfy the relationship.
(b) What put–call parity relationship exists between the price of a European call on a put and a European put on a put? Show that the formulas given in the text satisfy the relationship.