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:
“In short I must confide in you to take such care of the men under you as an economical householder would of his own family, doing every thing within himself as far as he can, and calling for as few supplies as possible. The less you depend for supplies from this quarter, the less you will be disappointed.”
—Thomas Jefferson (1743–1826)
“As a novelist, I cannot occupy myself with “characters,” or at any rate central ones, who lack panache, in one or another sense, who would be incapable of a major action or a major passion, or who have not a touch of the ambiguity, the ultimate unaccountability, the enlarging mistiness of persons “in history.” History, as more austerely I now know it, is not romantic. But I am.”
—Elizabeth Bowen (1899–1973)