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.