  We present a multivariate stochastic volatility model with leverage, which is
flexible enough to recapture the individual dynamics as well as the
interdependencies between several assets while still being highly analytically
tractable.
  First we derive the characteristic function and give conditions that ensure
its analyticity and absolute integrability in some open complex strip around
zero. Therefore we can use Fourier methods to compute the prices of multi-asset
options efficiently. To show the applicability of our results, we propose a
concrete specification, the OU-Wishart model, where the dynamics of each
individual asset coincide with the popular Gamma-OU BNS model. This model can
be well calibrated to market prices, which we illustrate with an example using
options on the exchange rates of some major currencies. Finally, we show that
covariance swaps can also be priced in closed form.
