Augustyniak, Maciej creator Badescu, Alexandru Bégin, Jean-François Jayaraman, Sarath Kumar text Amsterdam Elsevier B.V. 2024 continuing eng Abstract : This article studies the impact of fractional integration on volatility modelling and option pricing. We propose a general discrete-time pricing framework based on affine multi-component volatility models that admit ARCH( ) representations. This not only nests a large variety of option pricing models from the literature, but also allows for the introduction of novel covariance-stationary long-memory affine GARCH pricing models. Using an infinite sum characterization of the log-asset price’s cumulant generating function, we derive semi-explicit expressions for the valuation of European-style derivatives under a general variance-dependent stochastic discount factor. Moreover, we carry out an extensive empirical analysis using returns and S&P 500 options over the period 1996–2019. Overall, we find that once the informational content from options is incorporated into the parameter estimation process, the inclusion of fractionally integrated dynamics in volatility is beneficial for improving the out-of-sample option pricing performance. The largest improvements in the implied volatility root-mean-square errors occur for options with maturities longer than one year, reaching 28% and 18% when compared to standard one- and two-component short-memory models, respectively. Maciej Augustyniak [and three others]. Includes bibliographical references. Pricing Fractional affine models ARCH(∞) representations Volatility components Variance-dependent pricing kernels Joint estimation Research Quantitative research Journal articles (Open access) , volume 171 (February 2025). 1872-6372 https://www.sciencedirect.com/science/article/pii/S0378426624002607 https://www.sciencedirect.com/science/article/pii/S0378426624002607 250224 20250331033815.0