  We introduce an approximation strategy for the discounted moments of a
stochastic process that can, for a large class of problems, approximate the
true moments. These moments appear in pricing formulas of financial products
such as bonds and credit derivatives. The approximation relies on high-order
power series expansion of the infinitesimal generator, and draws parallels with
the theory of polynomial processes. We demonstrate applications to bond pricing
and credit derivatives. In the special cases that allow for an analytical
solution the approximation error decreases to around 10 to 100 times machine
precision for higher orders. When no analytical solution exists we tie out the
approximation with Monte Carlo simulations.
