[Journal:] International Journal of Financial Studies [ISSN:] 2227-7072 [Volume:] 5 [Year:] 2017 [Issue:] 1 [Pages:] 1-10
In this paper, an Adjustable Rate Mortgage (ARM) and a Fixed Rate Mortgage (FRM) are formalized and studied in a simple continuous-time setting under the assumption of a simple one-factor Affine Term Structure (ATS). Through an application of existing results from ATS theory, it is shown that when the short rate reaches a certain pre-determined boundary, the constant payment stream on a new FRM equals the payments on an existing ARM. Hereby, this paper provides a theoretical build-in cap on the formalized ARM. The finite boundary for the short-rate suggests that certain caps on ARMs should (in theory) be offered free of charge.
capped adjustable rate mortgages one-factor short rate models affine term structures