A0988
Title: A general option pricing framework for affine fractionally integrated models
Authors: Maciej Augustyniak - University of Montreal (Canada)
Alex Badescu - University of Calgary (Canada) [presenting]
Jean-Francois Begin - Simon Fraser University (Canada)
Sarath Kumar Jayaraman - University of Calgary (Canada)
Abstract: The purpose is to study the impact of fractional integration on volatility modelling and option pricing. A general discrete-time pricing framework is proposed based on affine multi-component volatility models. It 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 prices cumulant generating function, semi-explicit expressions are derived for the valuation of European-style derivatives under a general variance-dependent stochastic discount factor. Moreover, an extensive empirical analysis is carried out using returns and S\&P 500 options from 1996-2019. Overall, once the informational content from options is incorporated into the parameter estimation process, including fractionally integrated dynamics in volatility, the out-of-sample option pricing performance is improved. The largest improvements in the implied volatility root-mean-square errors occur for options with maturities longer than one year, reaching 33\% and 13\% when compared to standard one- and two-component short-memory models, respectively.
