Volatility long memory is a stylized fact that has been documented for a long time. Existing literature have two ways to model volatility long memory: component volatility models
and fractionally integrated volatility models. This paper develops a new fractionally integrated GARCH model, and investigates its performance by using the Standard and Poor’s
500 index returns and cross-sectional European option data. The fractionally integrated
GARCH model signi?cantly outperforms the simple GARCH(1, 1) model by generating 37%
less option pricing errors. With stronger volatility persistence, it also dominates a component volatility model, who has enjoyed a reputation for its outstanding option pricing
performance, by generating 15% less option pricing errors. We also con?rm the fractionally
integrated GARCH model’s robustness with the latest option prices. This paper indicates
that capturing volatility persistence represents a very promising direction for future study.
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