Co-moments of asset returns play a major role in financial contagion during crises. We study the properties of a particular specification of the generalized bivariate normal distribution which allows for co-volatility and co-skewness. With this probability distribution, formulae for single-name and exchange options can be evaluated quickly since they are based on one-dimensional integrals. We provide a very precise approximation formula for spread option prices and derive the corresponding greeks. We perform a day-to-day re-estimation of the probability distribution on a dataset of WTI vs Brent spread options, showing the ability of this specification to capture the salient empirical features observed in the market. Finally, we show the impact of co-movements on portfolio risk management.