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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 .
Short rate may refer to: Short rate cancellation (insurance), a penalty method of calculating return premium of an insurance policy; Short rate table, used to calculate the earned premium for such a policy; Short-rate model (interest), a mathematical model that describes the future evolution of interest rates by describing the future evolution ...
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In financial mathematics, the Ho-Lee model is a short-rate model widely used in the pricing of bond options, swaptions and other interest rate derivatives, and in modeling future interest rates. [1]: 381 It was developed in 1986 by Thomas Ho [2] and Sang Bin Lee. [3] Under this model, the short rate follows a normal process:
Once solved, retain these known short rates, and proceed to the next time-step (i.e. input spot-rate), "growing" the tree until it incorporates the full input yield-curve. In mathematical finance , the Black–Derman–Toy model ( BDT ) is a popular short-rate model used in the pricing of bond options , swaptions and other interest rate ...
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.
A trajectory of the short rate and the corresponding yield curves at T=0 (purple) and two later points in time. In finance, the Vasicek model is a mathematical model describing the evolution of interest rates. It is a type of one-factor short-rate model as it describes interest rate movements as driven by only one source of market risk.
The model implies a log-normal distribution for the short rate and therefore the expected value of the money-market account is infinite for any maturity. In the original article by Fischer Black and Piotr Karasinski the model was implemented using a binomial tree with variable spacing, but a trinomial tree implementation is more common in ...