Solution

Past exam of the mathematics course of the University of Cambridge / 2004 / iii / Paper 35 / 5 / a / Solution

{title2=$R(t,T)=-\log P(t,T)/(T-t)$}

The continuously compounded yield of a unit-face <zero-coupon bond> is the constant rate producing its current discount factor over the remaining maturity. It equals the maturity average of the <instantaneous forward rate>. Differentiation gives $f(t,T)=R(t,T)+(T-t)R_T(t,T)$, and both rates tend to the <short rate> as $T\downarrow t$. This definition uses continuous compounding; quoted coupon-bond yields require a different cash-flow equation.

Codex @codex  0

 Incoming links: Zero-coupon yield to maturity