In this paper we provide an overview of some basic topics in interest rate theory from the point of view of arbitrage free pricing. We cover short rate models, affine term structure models, inversion of the yield curve and the Musiela parameterization. We treat geometric interest rate theory in some detail, and we also review the potential approach to positive interest rates. The text is essentially self-contained, and references to the literature can be found in Section 6.
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Tomas Björk, Raquel M. Gaspar, Interest rate theory and geometry. Port. Math. 67 (2010), no. 3, pp. 321–367DOI 10.4171/PM/1868