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
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Famous quotes containing the words short and/or rate:
“The individual, the great artist when he comes, uses everything that has been discovered or known about his art up to that point, being able to accept or reject in a time so short it seems that the knowledge was born with him, rather than that he takes instantly what it takes the ordinary man a lifetime to know, and then the great artist goes beyond what has been done or known and makes something of his own.”
—Ernest Hemingway (1899–1961)
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—Leontine Young (20th century)