  In this paper we study the pricing of exchange options under a dynamic
described by stochastic correlation with random jumps. In particular, we
consider a Ornstein-Uhlenbeck covariance model with Levy Background Noise
Process driven by Inverse Gaussian subordinators. We use expansion in terms of
Taylor polynomials and cubic splines to approximately compute the price of the
derivative contract. Our findings show that this approach provides an efficient
way to compute the price when compared with a Monte Carlo method while
maintaining an equivalent degree of accuracy with the latter.
