  Models which postulate lognormal dynamics for interest rates which are
compounded according to market conventions, such as forward LIBOR or forward
swap rates, can be constructed initially in a discrete tenor framework.
Interpolating interest rates between maturities in the discrete tenor structure
is equivalent to extending the model to continuous tenor. The present paper
sets forth an alternative way of performing this extension; one which preserves
the Markovian properties of the discrete tenor models and guarantees the
positivity of all interpolated rates.
