"Faith does not merely mean that the soul realizes that the divine word is full of grace, free and holy; it also unites the soul with Christ, as a bride is united with her bridegroom. From such a marriage, as St. Paul says, it follows that Christ and the soul become one body, so that they hold all things in common, whether for better or worse. This means that what Christ possesses belongs to the believing soul; and what the soul possesses belongs to Christ. Thus Christ possesses all good things and holiness; these now belong to the soul. The soul possesses lots of vice and sin; these now belong to Christ. Here we have a sweet exchange and struggle. Christ is God and human being, who has never sinned and who's holiness is unconquerable, eternal and almighty. So he makes the sin of the living soul his own through its wedding ring, which is faith, and acts as if he had done it himself, so that sin could be swallowed up in him. For his unconquerable righteousness is too strong for all sin, so that it is made single and free from all its sins on account of its pledge, that is its faith, and can turn to the eternal righteousness of its bridegroom, Christ. Now is this not a happy business? Christ, the rich, noble, holy bridegroom, takes in marriage this poor, contemptible and sinful little prostitute, takes away all her evil, and bestows all his goodness upon her! It is no longer possible for sin to overwhelm her, for she is now found in Christ and is swallowed up by him, so that she possesses a rich righteousness in her bridegroom."
Martin Luther, as quoted by Alister McGrath in The Christian Theology Reader, p441 (I can't find where McGrath has taken this quote from; either my eyes are deceiving me or he has made an error in his referencing).
Note - For Luther the 'happy exchange' is rendered possible by the ultimate happy exchange that took place in the Incarnation, in which a real 'communication of attributes' (communicatio idiomatum) between the divine and human natures in the Person of Christ took place. This is a facet of Lutheran Christology which rests on the reception and development of the orthodox Chalcedonian Christology, and by which the Lutherans attempted to move beyond the impasse between the ancient Antiochian and Alexandrian Christologies (see Nestorius, Eutyches, et al in the usual theological dictionaries).
Both the Reformed and the Roman Catholics reject the Lutheran Christology, and in particular the communicatio maiestaticum (the communication of divine attributes to the human nature of Christ's Person), mistakenly accusing the Lutherans of distorting the true human nature of Christ by attributing divine attributes to it (for the classic Lutheran defence, see Chemnitz). The Lutheran doctrine of the communication of attributes was all but forgotten by Lutherans in the 20th century, except among the "old Lutherans" in Europe and the New World who consciously maintained the orthodox Lutheran theology (e.g. see Pieper's treatment in the second volume of his dogmatics). Lately, it has been the subject of exploration and renewal by theologians such as Bayer & Steiger.
For further reading on this subject see:
Martin Luther, The Freedom of a Christian (1520), Lectures on Galatians, Large Catechism (Article 2).
Oswald Bayer, Martin Luther's Theology (Eerdmans, 2008), 10.2 & 10.4
Martin Chemnitz, The Two Natures of Christ (Concordia,1971)
Richard A. Muller, 'communicatio idiomatum', in Dictionary of Latin and Greek Theological Terms (Paternoster, 1985) [not just a dictionary, but an indispensable handbook for the study of Lutheran & Reformed orthodoxy]
Francis Pieper, Christian Dogmatics (Concordia, 1951), Vol. II, p129ff
John Schaller, Biblical Christology (Northwestern, 1981)
[Schaller is especially clear on the scriptural foundations of all facets of the Lutheran Christology.]
Johann Anselm Steiger, “The communio idiomatum as the Axle and Motor of Luther’s Theology”, Lutheran Quarterly (Summer 2000), 125-158.