(17)
Conditional Expectation of the Forward Rate (CEFR). In
addition to the two endpoints, we can further enhance our estimate based
on the dynamics of the forward rates. The forward rate follows the
dynamic (9) (The drift term is ignored). We can derive the expectation
of the forward rate conditional on the two endpoints and replace the
random forward rate in the drift by the conditional expectation of the
forward rate.
Proposition 1. Assume the forward ratefollows the dynamic (9), with the two known endpoints given byand . Based on the conditional expectation of the forward
rate , the drift of can be expressed as