Skewness sign discrepancy in Marketron-calibrated log-returns

Determine, within the Marketron model calibrated to SPX option prices, whether the implied distribution of S&P 500 index log-returns exhibits positive or negative skewness across short and long horizons, and reconcile this with the negative skewness obtained when calibrating the Marketron model to historical S&P 500 equity time-series. Provide a clear characterization of conditions under which each sign arises and establish which sign is correct for the 2017–2020 period considered.

Background

The paper calibrates the Marketron model to SPX option prices and evaluates whether the model can simultaneously reproduce statistical properties of the underlying S&P 500 index log-returns. Simulation using parameters calibrated to options produces positive skewness at longer horizons, whereas prior work calibrating the Marketron model to S&P 500 equity time-series over 25 years reported negative skewness across horizons.

The authors note conflicting evidence in the literature: persistent negative skewness in aggregate returns (e.g., Neuberger and Payne, 2019) versus periods of positive realized skewness (e.g., 2017–2021) and compounding effects that can induce positive skewness at long horizons (Farago, 2023). The observed discrepancy motivates a focused investigation to determine which sign is appropriate in the specific period studied and under the Marketron framework.