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:
“No man will ever bring out of that office the reputation which carries him into it. The honeymoon would be as short in that case as in any other, and its moments of ecstasy would be ransomed by years of torment and hatred.”
—Thomas Jefferson (1743–1826)
“Whoever thinks his friend more important than his country, I rate him nowhere.”
—Sophocles (497–406/5 B.C.)