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:
“Jealousy is never satisfied with anything short of an omniscience that would detect the subtlest fold of the heart.”
—George Eliot [Mary Ann (or Marian)
“If you could choose your parents,... we would rather have a mother who felt a sense of guilt—at any rate who felt responsible, and felt that if things went wrong it was probably her fault—we’d rather have that than a mother who immediately turned to an outside thing to explain everything, and said it was due to the thunderstorm last night or some quite outside phenomenon and didn’t take responsibility for anything.”
—D.W. Winnicott (20th century)