It is very well known that one can derive rates for the decay of correlations of stationary stochastic processes arising from dynamical systems admitting a Young tower. Moreover, these rates depend on the volume decay of the points that take a long time before they return to the base of the tower. In this work we exploit the connection between decay of correlations of certain classes of observables and large deviations estimates of the stochastic processes obtained by evaluating these observables along the orbits of the system. We also show the relation between the large deviations of the logarithm of the derivative and the volume decay of the tail set of hyperbolic times (the set of points that resist to present hyperbolic behaviour in short time range). Based on these considerations we obtain a converse of L. S. Young's result, namely, if we have a system with a certain rate of decay of correlations then the system admits a Young tower with the same type of rate for the volume decay of the points with large return times. Moreover, we can show how to obtain an estimate for the large deviations of a whole class of observable functions, when we only have an estimate for the large deviations of the logarithm of the derivative.