After looking at @Affable Geek's answer to an overview question on different understandings of why Jesus had to die, and in particular after his comment on Catholicism in this respect, I went to look at the discussion in the Catechism of the Catholic Church regarding the role of the death of Jesus in salvation. .
One thing that struck me about the Catechism's discussion of "Why did Jesus die?" is the intimate connection the Catechism draws between the offering of Jesus on the Cross and the institution of the New Covenant. This connection is evident in the language of paragraph 610,
On the eve of his Passion, while still free, Jesus transformed this Last Supper with the apostles into the memorial of his voluntary offering to the Father for the salvation of men: "This is my body which is given for you." "This is my blood of the covenant, which is poured out for many for the forgiveness of sins."
and also in the language of the Eucharistic Prayer:
When supper was ended,
he took the chalice1 and, once more giving thanks,
he gave it to his disciples, saying:
Take this, all of you, and drink from it:
for this is the chalice of my Blood,
the Blood of the new and eternal covenant,
which will be poured out for you and for many
for the forgiveness of sins.
That is, rather than specifying a single reason why Jesus had to die (was it as a ransom from sin? an atonement for humanity?), Catholicism appears to focus instead on the New Covenant between God and Man which His death and resurrection created.
I don't see this connection being made in the soteriological approaches discussed in the answer above. How does Reformed Theology in particular connect its view of the purpose behind Jesus' death with the institution of the New Covenant? Or does Reformed Theology not talk much about the New Covenant? What sort of emphasis does it place on any connection between the Covenant and the Sacrifice?
1 There are a number of difficulties I have with the new translation of the Roman Missal; one is the translation of "calix" as "chalice" rather than the simple "cup" of the previous translation.