A random matching model with money is used to study the nominal yield on small denomination, bearer, safe, discount securities issued by the government. There is always one steady state with matured securities circulating at par and, for some parameters, another with them circulating at a discount. In the former, a necessary and sufficient condition for a positive nominal yield on not-yet-matured securities is exogenous discriminatory treatment of them by the government. In the latter, the post-maturity discount on securities induces a deeper pre-maturity discount even without such discriminatory treatment.

A pairwise random meeting model with money is used to study the nominal yield on pure-discount, default-free securities that are issued by the government. There is one steady state with matured securities at par and, for some parameters, another with them at a discount. In the former, exogenous rejection of unmatured securities by the government is necessary and sufficient for such a steady state to display a positive nominal yield on unmatured securities. In the latter, the post-maturity discount on securities induces a deeper pre-maturity discount even if there is no exogenous rejection of unmatured securities.