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:
“And were an epitaph to be my story
I’d have a short one ready for my own.
I would have written of me on my stone:
I had a lover’s quarrel with the world.”
—Robert Frost (1874–1963)
“Put God in your debt. Every stroke shall be repaid. The longer the payment is withholden, the better for you; for compound interest on compound interest is the rate and usage of this exchequer.”
—Ralph Waldo Emerson (1803–1882)