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Under a short rate model, the stochastic state variable is taken to be the instantaneous spot rate. [1] The short rate, , then, is the (continuously compounded, annualized) interest rate at which an entity can borrow money for an infinitesimally short period of time from time .
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 ...
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 ...
Because interest rate caps/floors are equivalent to bond puts and calls respectively, the above analysis shows that caps and floors can be priced analytically in the Hull–White model. Jamshidian's trick applies to Hull–White (as today's value of a swaption in the Hull–White model is a monotonic function of today's short rate).
A more tractable approach is in Brigo and Mercurio (2001b) [4] where an external time-dependent shift is added to the model for consistency with an input term structure of rates. A significant extension of the CIR model to the case of stochastic mean and stochastic volatility is given by Lin Chen (1996) and is known as Chen model.
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 ...
Time series analysis comprises methods for analyzing time series data in order to extract meaningful statistics and other characteristics of the data. Time series forecasting is the use of a model to predict future values based on previously observed values.
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.