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% Author: Simon-Pierre Boucher
% Contact: contact@spboucher.ai
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\section{Discussion}\label{sec:discuss}

\subsection{Economic Interpretation}

\paragraph{Horizon-dependent predictability.}
The increase from near-zero daily $R^2$ to 4.8--19.3\% weekly $R^2$ suggests that option-implied information captures medium-term risk assessments that take several days to be reflected in spot prices, consistent with limits to arbitrage and gradual information diffusion.

\paragraph{Implied kurtosis as the strongest predictor.}
The Sharpe ratio of 2.33 for the kurtosis sort points to a ``kurtosis risk premium'': investors demand compensation for holding assets with uncertain tail behavior. This extends the variance-risk-premium literature \citep{bollerslev2009expected} to higher moments.

\paragraph{Information flow: options lead volatility.}
The Granger causality results ($F=62.4$, significant for 100\% of tickers) and the variance decomposition (73.8\% at 20 days) establish the options market as the dominant information venue for volatility dynamics, consistent with the informational-role hypothesis of \citet{easley1998option}.

\paragraph{The failure of the price-magnet hypothesis.}
The 47.0\% convergence rate---below the 50\% null---contradicts the ``max pain'' narrative and is consistent with \citet{avellaneda2003weighted}, who find that pinning is confined to the last hours before expiration.

\subsection{Comparison with Prior Literature}

The implied-kurtosis Sharpe ratio of 2.33 exceeds those of the variance-risk-premium strategies in \citet{bollerslev2009expected} ($\approx$1.0) and the skewness sorts in \citet{xing2010does} ($\approx$0.8). The HAR-RV~$+$~IV improvement (23.3\%) likewise exceeds the 10--15\% reported by \citet{busch2011role}, plausibly because the present study exploits the full surface rather than a single VIX-like measure.

\subsection{Limitations}

Several limitations merit acknowledgment. Portfolio sorts assume frictionless trading. The options features are computed from end-of-day data; intraday options data might reveal different patterns. The focus on large-cap, liquid names may limit generalizability. The implied-correlation analysis uses equal weights. Finally, the machine-learning comparison is limited to tree-based methods; deep learning merits future investigation.