Comovements among asset prices have received a lot of attention for several reasons. For example, comovements are important in cross-hedging and cross-speculation; they determine capital allocation both domestically and in international mean-variance portfolios and also, they are useful in investigating the extent of integration among financial markets. In this paper we propose a new methodology for the non-linear modelling of bivariate comovements. Our approach extends the ones presented in the recent literature. In fact, our methodology, outlined in three steps, allows the evaluation and the statistical testing of non-linearly driven comovements between two given random variables. Moreover, when such a bivariate dependence relationship is detected, our approach creates a polynomial approximation. We illustrate our three-step methodology to the time series of energy related asset prices. Finally, we exploit this dependence relationship and its polynomial approximation to obtain analytical approximations of the Greeks for the European call and put options in terms of an asset whose price comoves with the price of the underlying asset.