  We consider a class of assets whose risk-neutral pricing dynamics are
described by an exponential L\'evy-type process subject to default. The class
of processes we consider features locally-dependent drift, diffusion and
default-intensity as well as a locally-dependent L\'evy measure. Using
techniques from regular perturbation theory and Fourier analysis, we derive a
series expansion for the price of a European-style option. We also provide
precise conditions under which this series expansion converges to the exact
price. Additionally, for a certain subclass of assets in our modeling
framework, we derive an expansion for the implied volatility induced by our
option pricing formula. The implied volatility expansion is exact within its
radius of convergence. As an example of our framework, we propose a class of
CEV-like L\'evy-type models. Within this class, approximate option prices can
be computed by a single Fourier integral and approximate implied volatilities
are explicit (i.e., no integration is required). Furthermore, the class of
CEV-like L\'evy-type models is shown to provide a tight fit to the implied
volatility surface of S{&}P500 index options.
