(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