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:
“For the theatre one needs long arms; it is better to have them too long than too short. An artiste with short arms can never, never make a fine gesture.”
—Sarah Bernhardt (1844–1923)
“Strange that the vanity which accompanies beauty—excusable, perhaps, when there is such great beauty, or at any rate understandable—should persist after the beauty was gone.”
—Mary A. [Elizabeth, Countess Von] Arnim (1866–1941)