  We consider the supOU stochastic volatility model which is able to exhibit
long-range dependence. For this model we give conditions for the discounted
stock price to be a martingale, calculate the characteristic function, give a
strip where it is analytic and discuss the use of Fourier pricing techniques.
  Finally, we present a concrete specification with polynomially decaying
autocorrelations and calibrate it to observed market prices of plain vanilla
options.
