## Glossary

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# Zero coupon bond

A zero coupon bond (ZCB) is a binding contract who pays one unit of currency at some pre-specified future time $T$. $T$ is called maturity time. The ZCB is also called a pure discount bond. If the interest rate is positive, (which it is in realistic cases), the value of ZCB is always less then one before time $T$. If the interest rate (short rate) is constant, r say, the value of the ZCB at a time $t$ than maturity time $T$, $p(t,T)$ equals $e^{-r(T-t)}$. If we model the short rate with an affine term structure model the value of the ZCB is given by $p(t,T)=e^{A(t,T)-r(t)B(t,T)},$ where A and B are deterministic functions satisfying a system of ordinary differential equations. Since $P(T,T)\equiv 1$ for all $r(T)$ we must have that $A(T,T)=0$ and $B(T,T)=0$.

The central banks issue contracts of ZCB-type on a regular basis. These contracts are then called treasury bills or T-Bills for short. The maturity times are usually less or equal to one year. For longer maturities usually coupon bonds are issued. These contracts are called treasury bonds.