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Dynamics of Interest Cash Flows From a Bank’s Loan Portfolio with Continuously Distributed Maturities

A continuous-time deterministic model for analytical simulation of impact of the change in yield curve on bank’s interest income from a fixed rate loans portfolio is presented. It is considered both differential and integral presentations of equations for dynamics of principal and interest cash flows. The model allows taking into account the arbitrary movements in interest rates. Examples of calculation of total (from portfolio) and partial (across maturities) interest cash flows and corresponding interest rates on those cash flows are given. The sensitivity of total interest cash flows is evaluated for some changes in yield curve on loans that obeys the Nelson-Siegel model.