This article studies the impact of long memory on modelling asset returns and pricing options in discrete-time. We propose a general pricing framework based on affine multi-component volatility models that admit ARCH(∞) representations, which not only nests a plethora of option pricing models from the literature, but also allows for the introduction of novel fractionally integrated processes for valuation purposes. We carry out an extensive empirical analysis which includes single and joint calibrations of a variety of short and long memory models to historical returns and S&P 500 options. Our results indicate that the inclusion of long memory into modelling the returns substantially improves the option pricing performance. Moreover, using an expanding window out-of-sample exercise, we show that a single-component long-memory model outperforms a richer-parametrized two-component model with short-memory dynamics, the difference becoming even larger when combining the two features.