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Title: Long memory in option pricing: A fractional discrete-time approach Authors:  Maciej Augustyniak - University of Montreal (Canada)
Alex Badescu - University of Calgary (Canada)
Jean Francois Begin - Simon Fraser University (Canada) [presenting]
Sarath Kumar Jayaraman - University of Calgary (Canada)
Abstract: The impact of long memory on asset return modelling and option pricing is studied. We propose a general discrete-time pricing framework based on affine multi-component volatility models that admit ARCH($\infty$) representations. It not only nests a plethora of option pricing models from the literature but also allows for the introduction of novel fractionally integrated processes for option valuation purposes. Using an infinite sum characterization of the unconditional cumulant generating function of the log-asset price, we derive semi-explicit expressions for European option prices under a volatility-dependent stochastic discount factor. We carry out an extensive empirical analysis which includes returns-only as well as return and option joint estimations of a variety of short- and long-memory models for the S&P 500 index. Our results indicate that the inclusion of long memory into return modelling substantially improves the option pricing performance. Using a set of out-of-sample option pricing errors, we show that long-memory models outperform richer-parametrized one- and two-component models with short-memory dynamics.