  It is known that the implied volatility skew of FX options demonstrates a
stochastic behavior which is called stochastic skew. In this paper we create
stochastic skew by assuming the spot/instantaneous variance correlation to be
stochastic. Accordingly, we consider a class of SLV models with stochastic
correlation where all drivers - the spot, instantaneous variance and their
correlation are modeled by Levy processes. We assume all diffusion components
to be fully correlated as well as all jump components. A new fully implicit
splitting finite-difference scheme is proposed for solving forward PIDE which
is used when calibrating the model to market prices of the FX options with
different strikes and maturities. The scheme is unconditionally stable, of
second order of approximation in time and space, and achieves a linear
complexity in each spatial direction. The results of simulation obtained by
using this model demonstrate capacity of the presented approach in modeling
stochastic skew.
