  In this article we focus on the pricing of exchange options when the dynamic
of logprices follows either the well-known variance gamma or the recent
variance gamma++ process introduced in Gardini et al [19]. In particular, for
the former model we can derive a Margrabe's type formula whereas, for the
latter one we can write an "integral free" formula. Furthermore, we show how to
construct a general multidimensional versions of the variance gamma++ processes
preserving both the mathematical and numerical tractability. Finally we apply
the derived models to German and French energy power markets: we calibrate
their parameters using real market data and we accordingly evaluate exchange
options with the derived closed formulas, Fourier based methods and Monte Carlo
techniques.
