I. ORIGIN OF THE SATISFACTION THEORY OF THE ATONEMENT (from Church historian Jaroslav Pelikan):
II. AN UNSATISFACTORY LIMITATION OF SATISFACTION THEORY
The Westminster Confession says the crucifixion of Christ “hath fully satisfied the justice of his Father; and purchased not only reconciliation, but an everlasting inheritance in the kingdom of heaven for all those whom the Father hath given unto Him.”
“Satisfaction” in the Reformed Confessions, as Reformed theologian Charles Hodge explains, represents “a perfect satisfaction, so that justice has no further demands…” the crucifixion of Christ alone as a full and absolutely comprehensive satisfaction “met and answered all the demands of God’s law and justice against the sinner… This is what is called the perfection of Christ’s satisfaction. It perfectly, from its own intrinsic worth, satisfies the demands of justice… It follows from the perfection of Christ’s satisfaction that it supersedes and renders impossible all other satisfactions for sin” (Charles Hodge, Systematic Theology, Vol II., Ch 4, “The Satisfaction of Christ”).
According to this model the cross of Christ alone “satisfies” absolutely every divine requirement for reconciliation. Nothing else, absolutely nothing else, needed. One might well expect St. Paul, on this model, should have written “If Christ has not been raised, since the cross alone is “satisfactory” to expiate your sins, you are delivered from your sins regardless.” But St. Paul affirmed the very opposite:
“If Christ has not been raised… you are still in your sins” (1 Cor 15:17). If Christ had only died, but had not been raised, His death alone would not be “satisfactory” for the expiation of sins, according to St. Paul.
This emphasis upon the absolute soteriological necessity of the resurrection is also found in Paul’s letter to the Romans: “He was delivered over to death for our sins and was raised to life for our justification” (Rom 4:25).
Joel B Green of Asbury Seminary in Kentucky observes, “because of the singular focus on penal satisfaction, Jesus’ resurrection is not really necessary according to this model” (Joel B. Green and Mark D. Baker, Recovering the Scandal of the Cross (Downers Grove: IVP, 2000), p. 148).
But why would the resurrection be such an absolute soteriological necessity, as St. Paul undeniably does present it, for the expiation of sin?
Going back before the medieval origin of the Satisfaction Theory we find the paleo-orthodox / patristic writers had a different, and fuller view of reconciliation with God “in Christ.” It involved actual mystical union, a living fellowship or communion (koinonia), with the living Christ: salvation consisted in His actual glorifying presence. It would on this view be a bizarre contradiction to suggest a dead savior was “satisfactory”; if the savior was merely dead, there would be no one to be in Union with, no glorifying presence, no theosis! (which is what the early fathers conceived salvation to be). On this model it is perfectly understandable to affirm “If Christ has not been raised… you are still in your sins” (1 Cor 15:17). Without a living Christ there would be no living union with Christ, which is what the early fathers universally understood salvation to be.
We do not worship a dead victim, but a Living Victor, who lives and presently intercedes.
A dead vine can produce no fruit, but only a living one: “I am the true vine…” Except our Savior were risen and alive it would be impossible to “Remain in me, as I also remain in you. No branch can bear fruit by itself; it must remain in the vine. Neither can you bear fruit unless you remain in me” (Jn 15:4).
 The Westminister Confession, Ch 8.5. [Reformed/Calvinist; other Reformed Confessions affirming the Satisfaction Theory include Second Helvetic Confession, The Heidelberg Catechism, Formula Consensus Helvetica, The Satisfaction Theory of the Atonement is also affirmed in The Augsburg Confession and Formula of Concord (Lutheran), and in the Roman Catholic Council of Trent. Since that time many within various trajectories of Protestantism have questioned the Satisfaction Theory
See also the related article: “Propitiation or Expiation: Did Christ Change God’s Attitude?” https://katachriston.wordpress.com/2011/06/22/propitiation-or-expiation-did-christ-change-gods-attitude/