Systems, methods, and computer-readable media are disclosed for calculating input-output relationships using, for example, spline functions. In accordance with one implementation, a computer-implemented method is provided that includes determining at least one price-volume point comprising a price and associated volume, transforming the price, and using the transformed price to calculate values along a spline function to obtain a price-volume curve weight factor. The method further includes transforming a second price, calculating values along the spline function and the first derivative of the spline function using the transformed second price to obtain a volume estimate and volume rate at the second price, and recalculating the spline function based on the calculated price-volume curve weight factor, volume estimate, volume estimate and volume rate.