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Differential equation involving bond price and forward rate
Given forward rate f(t,T) and bond price P(t,T) where
$f(t,T) = - \frac{\partial}{\partial T} \ln P(t,T)$,
$P(T,T) = 1 = P(t,t)$,
T>0 and
$t \in [0,T]$
Does it follow that $P(t,T) = exp(-\int_{t}^...