  We consider a defaultable asset whose risk-neutral pricing dynamics are
described by an exponential Levy-type martingale subject to default. This class
of models allows for local volatility, local default intensity, and a locally
dependent Levy measure. Generalizing and extending the novel adjoint expansion
technique of Pagliarani, Pascucci, and Riga (2013), we derive a family of
asymptotic expansions for the transition density of the underlying as well as
for European-style option prices and defaultable bond prices. For the density
expansion, we also provide error bounds for the truncated asymptotic series.
Our method is numerically efficient; approximate transition densities and
European option prices are computed via Fourier transforms; approximate bond
prices are computed as finite series. Additionally, as in Pagliarani et al.
(2013), for models with Gaussian-type jumps, approximate option prices can be
computed in closed form. Sample Mathematica code is provided.
