Valuing exchange options under an Ornstein-Uhlenbeck covariance model

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