A general option pricing framework for affine fractionally integrated models

Maciej Augustyniak, Alexandru Badescu, Jean-François Bégin and Sarath Kumar Jayaraman

Journal of Banking & Finance, 2025, vol. 171, issue C

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.

Keywords: Fractional affine models; ARCH(∞) representations; Volatility components; Variance-dependent pricing kernels; Joint estimation (search for similar items in EconPapers)
JEL-codes: C58 G12 G13 (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378426624002607
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:jbfina:v:171:y:2025:i:c:s0378426624002607

DOI: 10.1016/j.jbankfin.2024.107346

Access Statistics for this article

Journal of Banking & Finance is currently edited by Ike Mathur

More articles in Journal of Banking & Finance from Elsevier
Bibliographic data for series maintained by Catherine Liu ().