We consider a defaultable asset whose risk-neutral pricing dynamics are described by an exponential Lévy-type martingale subject to default. This class of models allows for local volatility, local default intensity, and a locally dependent Lévy measure. Generalizing and extending the novel...

We prove asymptotic convergence results for some analytical expansions of solutions of degenerate PDEs with applications to financial mathematics. In particular, we combine short-time and global-in-space error estimates, previously obtained in the uniformly parabolic case, with some a priori...

We consider a general d-dimensional Levy-type process with killing. Combining the classical Dyson series approach with a novel polynomial expansion of the generator A(t) of the Levy-type process, we derive a family of asymptotic approximations for transition densities and European-style options...

We find approximate solutions of partial integro-differential equations, which arise in financial models when defaultable assets are described by general scalar Levy-type stochastic processes. We derive rigorous error bounds for the approximate solutions. We also provide numerical examples...

We consider the Cauchy problem associated with a general parabolic partial differential equation in d dimensions. We find a family of closed-form asymptotic approximations for the unique classical solution of this equation as well as rigorous short-time error estimates. Using a boot-strapping...

We consider an asset whose risk-neutral dynamics are described by a general class of local-stochastic volatility models and derive a family of asymptotic expansions for European-style option prices and implied volatilities. Our implied volatility expansions are explicit; they do not require any...