  We introduce Dirac processes, using Dirac delta functions, for
short-rate-type pricing of financial derivatives. Dirac processes add spikes to
the existing building blocks of diffusions and jumps. Dirac processes are
Generalized Processes, which have not been used directly before because the
dollar value of non-Real numbers is meaningless. However, short-rate pricing is
based on integrals so Dirac processes are natural. This integration directly
implies that jumps are redundant whilst Dirac processes expand expressivity of
short-rate approaches. Practically, we demonstrate that Dirac processes enable
high implied volatility for CDS swaptions that has been otherwise problematic
in hazard rate setups.
