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6.2 Methods for American options: finite elements (FEM)

What appears to be a minor extension of the European contract results in considerable mathematical difficulties: so much in fact, that an explicit and exact pricing formula cannot anymore be found analytically. Fortunately, the variational calculus introduced in sect.5.3.1 to implement the finite element method provides a solid theoretical framework that can be extended to obtain a numerical solution with only minor changes to account for the difference in the European and American exercise styles.