The Short Rate
The short rate, is the (continuously compounded, annualized) interest rate at which an entity can borrow money for an infinitesimally short period of time from time t. Specifying the current short rate does not specify the entire yield curve. However no-arbitrage arguments show that, under some fairly relaxed technical conditions, if we model the evolution of as a stochastic process under a risk-neutral measure Q then the price at time t of a zero-coupon bond maturing at time T is given by
where is the natural filtration for the process. Thus specifying a model for the short rate specifies future bond prices. This means that instantaneous forward rates are also specified by the usual formula
Read more about this topic: Short-rate Model
Famous quotes containing the words short and/or rate:
“Our friendships hurry to short and poor conclusions, because we have made them a texture of wine and dreams, instead of the tough fibre of the human heart. The laws of friendship are austere and eternal, of one web with the laws of nature and of morals.”
—Ralph Waldo Emerson (1803–1882)
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—Mary A. [Elizabeth, Countess Von] Arnim (1866–1941)