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Tree returning the OAS (black vs red): the short rate is the top value; the development of the bond value shows pull-to-par clearly . A short-rate model, in the context of interest rate derivatives, is a mathematical model that describes the future evolution of interest rates by describing the future evolution of the short rate, usually written .
It is a one-factor model; that is, a single stochastic factor—the short rate—determines the future evolution of all interest rates. It was the first model to combine the mean-reverting behaviour of the short rate with the log-normal distribution, [1] and is still widely used. [2] [3]
Modeling of interest rate derivatives is usually done on a time-dependent multi-dimensional lattice ("tree") or using specialized simulation models. Both are calibrated to the underlying risk drivers, usually domestic or foreign short rates and foreign exchange market rates, and incorporate delivery- and day count conventions. The Heath ...
Pages in category "Short-rate models" The following 14 pages are in this category, out of 14 total. This list may not reflect recent changes. * Short-rate model; A.
In mathematical finance, the Cox–Ingersoll–Ross (CIR) model describes the evolution of interest rates. It is a type of "one factor model" (short-rate model) as it describes interest rate movements as driven by only one source of market risk. The model can be used in the valuation of interest rate derivatives.
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The HJM framework originates from the work of David Heath, Robert A. Jarrow, and Andrew Morton in the late 1980s, especially Bond pricing and the term structure of interest rates: a new methodology (1987) – working paper, Cornell University, and Bond pricing and the term structure of interest rates: a new methodology (1989) – working paper ...