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# Short rate

Short rate refers to the instantaneous interest rate payed over an infinitesimal time interval, i.e. interest=r(t)*dt*A, where r(t) is the short dt is the infinitesimal time interval and A is the amount of money you earn interest on.
So say that we put in one unit of currency into bank account at time zero and
then do not make any insertions or withdrawels then the amount of money in the bank account, B(t), will follow the ordinary differential equation.

dB(t)=r(t)B(t)dt,B(0)=1.

The solution is then B(t)=e^{0∫tr(s)ds}.

It is common to try to model the short rate with stochastic models such as e.g. Ho-Lee ,Vasicek , Hull-White CIR++ etc.

dB(t)=r(t)B(t)dt,B(0)=1.

The solution is then B(t)=e

It is common to try to model the short rate with stochastic models such as e.g. Ho-Lee ,Vasicek , Hull-White CIR++ etc.

Questions: Magnus Wiktorsson

Last update: 2009 Nov 11 14:52:47. Validate: HTML CSS

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