Long and Short Memory in the Risk-Neutral Pricing Process
Journal of Derivatives, Summer 2019, DOI: https://doi.org/10.3905/jod.2019.1.077
Posted: 28 Feb 2019 Last revised: 14 Sep 2021
Date Written: February 11, 2019
The paper proposes a semimartingale approximation to a fractional Levy processes that is capable of capturing long and short memory in the stochastic process together with fat tails. We use the semimartingale process in option pricing and empirically compare its performance to other option pricing models including a stochastic volatility Levy process. We contribute to the empirical literature by being the first to report the implied Hurst index computed from observed option prices using the Levy process model. Calibrating the implied Hurst index of S&P500 option prices in a period that covers the 2008 financial crisis, we find that the risk neutral measure is characterized by a short memory in turbulent markets and a long memory in calm markets.
Keywords: Option Pricing, Long-Range Dependence, Fractional Levy Processes
JEL Classification: C13, C22, G13
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