Achilles,

Shreve's books are specific to financial mathematics. You would likely study these books once you are on an MFE program. While he does address many of the mathematical and statistical topics that you would need as background for stochastic calculus, some of this material is quite abstract and it is extremely challenging if you are seeing it for the first time.

It is very helpful to obtain some familiarity with various stochastic processes so that when you come to them in Shreve you are not seeing them for the first time. The probability material which I have mentioned above, particularly the Sheldon Ross books, are materials that you would likely use if you were studying an (applied) statistics degree and would help you understand various statistical concepts which are not always covered in a financial mathematics degree, where limitations of time dictate that certain topics cannot be covered. However, as I mentioned above, Ross omits anything requiring measure theory.

What really trips people up if they don't have a strong background in pure mathematics is the real analysis material. If, when you enter an MFE course, you have already obtained an understanding of things like sigma-algebras, filtrations, convergence, the Lebesgue integral (vs. the Riemann integral with which everyone else is familiar), the various flavors of limits and convergence (in probability, in distribution, almost-everywhere, almost-surely, etc.) and the other aspects of Measure Theory, then it would be much easier for you to understand the financial concepts which are covered in Shreve. You would definitely cover this material in the first year of any mathematics Ph.D. program, and it should also be covered in a pure mathematics MS degree. People who are not pursuing such degrees may never see this material.

While it is possible to learn it all at the same time, doing so is quite challenging. It is much easier to master Shreve if you are seeing these concepts for the second (or third) time, rather than if you are seeing everything for the first time.