Marginal density expansions for diffusions and stochastic volatility, part II: Applications

In [17] we discussed density expansions for multidimensional diffusions ( X, . . . , X ) , at fixed time T and projected to their first l coordinates, in the small noise regime. Global conditions were found which replace the well-known ”not-in-cutlocus” condition known from heat-kernel asymptotics. In the present paper we discuss financial applications; these include tail and implied volatility asymptotics in some correlated stochastic volatility models. In particular, we solve a problem left open by A. Gulisashvili and E.M. Stein (2009).