I've been told by many people that Martin Luther referred to 2 Corinthians 5:21 as "The Great Exchange." But I've been unable to verify that Luther had ever actually used the term "The Great Exchange."
For our sake he made him to be sin who knew no sin, so that in him we might become the righteousness of God.
~ 2 Corinthians 5:21 ESV
Luther wasn't systematic in his writings, and there's a translation barrier since he wrote primarily in Latin and German. So it's possible he did use this phrase, "The Great Exchange" and maybe if someone has a citation, I'd be greatly indebted, but for the time being it seems that Luther never said the words "The Great Exchange". Even if "The Great Exchange" was a phrased coined by later theologians, the idea of the Satisfaction Atonement Theory as first conceived in Anslem's Cur Deus Homo has been advanced and expressed in many works of Luther in a similar way to Substitutionary Atonement.
Here is an example of "The Great Exchange" in Luther's works, even if it isn't explicitly called "The Great Exchange":
"Therefore, my dear brother, learn Christ and him crucified. Learn to pray to him an, despairing of yourself, say: "Thou, Lord Jesus, art my righteousness, but I am thy sin. Thou hast taken upon thyself what is mine and hast given to me what is thine. Thou has taken upon thyself what thou wast not and hast given to me what I was not." Beware of aspiring to such purity that you will not wish to be looked upon as a sinner, or to be one. For Christ dwells only in sinners. On this account he descended from heaven, where he dwelt among the righteous, to dwell among sinners. Meditate on this love of his and you will see his sweet consolation. For why was it necessary for him to die if we can obtain a good conscience by our works and afflictions? Accordingly you will find peace only in him and only when you despair of yourself and your own works. Besides, you will learn from him that just as he has received you, so he has made your sins his own and has made his righteousness."
"Instructions to the Perplexed and Doubting, To George Spenlein, April 8, 1516", Luther: Letters of Spiritual Counsel, Martin Luther, Theodore G. Tappert, Library of Christian Classics Vol 18. pg 110.
Wolfhart Pannenberg points to Martin Luther's The Freedom of a Christian" as an example of what he called the "Happy Exchange":
Who then can value highly enough these royal nuptials? Who can comprehend the riches of the glory of this grace? Christ, that rich and pious husband, takes as a wife a needy and impious harlot, redeeming her from all her evils, and supplying her with all His good things. It is impossible now that her sins should destroy her, since they have been laid upon Christ and swallowed up in Him, and since she has in her husband Christ a righteousness which she may claim as her own, and which she can set up with confidence against all her sins, against death and hell, saying: “If I have sinned, my Christ, in whom I believe, has not sinned; all mine is His, and all His is mine;” as it is written, “My beloved is mine, and I am his. (Songs 2:16) This is what Paul says: “Thanks be to God, which giveth us the victory through our Lord Jesus Christ;” victory over sin and death, as he says: “The sting of death is sin, and the strength of sin is the law.” (1 Cor 15:56-57) [..]
As Christ by His birthright has obtained these two dignities, so He imparts and communicates them to every believer in Him, under that law of matrimony of which we have spoken above, by which all that is the husband’s is also the wife’s. Hence all we who believe on Christ are kings and priests in Christ, as it is said: “Ye are a chosen generation, a royal priesthood, an holy nation, a peculiar people; that ye should shew forth the praises of him who hath called you out of darkness into his marvellous light.” (1 Pet 2:9)
- Martin Luther, De libertate christiana 1520, c. 12. WA7, pg.25f),
The closest quotation to the "Great Exchange" that I've been able to find is by John Calvin, whom in his Institutes IV.17.2 use the phrase: "Wondrous Exchange" and the Latin he used for Wonderous (or glorious) exchange is: mirifica commutatio.
"2. Pious souls can derive great confidence and delight from this sacrament, as being a testimony that they form one body with Christ, so that everything which is his they may call their own. Hence it follows, that we can confidently assure ourselves, that eternal life, of which he himself is the heir, is ours, and that the kingdom of heaven, into which he has entered, can no more be taken from us than from him; on the other hand, that we cannot be condemned for our sins, from the guilt of which he absolves us, seeing he has been pleased that these should be imputed to himself as if they were his own. This is the wondrous exchange (mirifica commutatio) made by his boundless goodness. Having become with us the Son of Man, he has made us with himself sons of God. By his own descent to the earth he has prepared our ascent to heaven. Having received our mortality, he has bestowed on us his immortality. Having undertaken our weakness, he has made us strong in his strength. Having submitted to our poverty, he has transferred to us his riches. Having taken upon himself the burden of unrighteousness with which we were oppressed, he has clothed us with his righteousness."
- John Calvin, Institutes IV.17.2,
Related: 2 corinthians 5:21, anslem, cur deus homo, Institutes, John Calvin, Martin Luther, mirifica commutatio, the great exchange, the wondrous exchange