% For submission to the Journal of Futures Markets (JFM)

\section{Figures}


\begin{landscape}
\begin{figure}[t]
\includegraphics[height=0.78\textheight,keepaspectratio]{oil_rv.pdf}
\centering
\caption{Realized volatility of the Crude Oil ETF and its iNAV. The figure plots daily realized volatility (sum of squared intraday log returns, $\times 10^{-3}$) for the USO ETF (blue) and its iNAV, proxied by the CL futures contract (red), from 2008-03-27 to 2025-08-01. Panels A, B, and C use returns sampled at the 1-minute, 5-minute, and 30-minute frequencies, respectively. For readability, each series is winsorized at its 99th percentile within each panel.}
\label{ch2:fig:rv_uso}
\end{figure}
\end{landscape}

\begin{landscape}
\begin{figure}[t]
\includegraphics[height=0.78\textheight,keepaspectratio]{gold_rv.pdf}
\centering
\caption{Realized volatility of the Gold ETF and its iNAV. The figure plots daily realized volatility (sum of squared intraday log returns, $\times 10^{-3}$) for the GLD ETF (blue) and its iNAV, proxied by the GC futures contract (red), from 2008-03-27 to 2025-08-01. Panels A, B, and C use returns sampled at the 1-minute, 5-minute, and 30-minute frequencies, respectively. For readability, each series is winsorized at its 99th percentile within each panel.}
\label{ch2:fig:rv_gld}
\end{figure}
\end{landscape}

\begin{landscape}
\begin{figure}[t]
\includegraphics[height=0.78\textheight,keepaspectratio]{silver_rv.pdf}
\centering
\caption{Realized volatility of the Silver ETF and its iNAV. The figure plots daily realized volatility (sum of squared intraday log returns, $\times 10^{-3}$) for the SLV ETF (blue) and its iNAV, proxied by the SI futures contract (red), from 2008-03-27 to 2025-08-01. Panels A, B, and C use returns sampled at the 1-minute, 5-minute, and 30-minute frequencies, respectively. For readability, each series is winsorized at its 99th percentile within each panel.}
\label{ch2:fig:rv_slv}
\end{figure}
\end{landscape}

\begin{landscape}
\begin{figure}[t]
\includegraphics[height=0.78\textheight,keepaspectratio]{gas_rv.pdf}
\centering
\caption{Realized volatility of the Natural Gas ETF and its iNAV. The figure plots daily realized volatility (sum of squared intraday log returns, $\times 10^{-3}$) for the UNG ETF (blue) and its iNAV, proxied by the NG futures contract (red), from 2008-03-27 to 2025-08-01. Panels A, B, and C use returns sampled at the 1-minute, 5-minute, and 30-minute frequencies, respectively. For readability, each series is winsorized at its 99th percentile within each panel.}
\label{ch2:fig:rv_ung}
\end{figure}
\end{landscape}


\begin{landscape}
\begin{figure}[t]
\includegraphics[width=16cm,trim=0 0 0 22,clip]{oil__uso_cl__irf.pdf}
\centering
\caption{Impulse Response Functions (IRF) for USO ETF and Crude Oil (CL) iNAV Volatility. Bayesian VAR impulse responses showing fast shock absorption with systematic asymmetry: iNAV shocks cause large and persistent responses in ETF volatility while ETF shocks generate smaller and more transitory effects on iNAV, validating bidirectional but asymmetric transmission in crude oil markets.}
\label{ch2:fig:irf1}
\end{figure}
\end{landscape}

\begin{landscape}
\begin{figure}[t]
\includegraphics[width=16cm,trim=0 0 0 22,clip]{gold__gld_gc__irf.pdf}
\centering
\caption{Impulse Response Functions (IRF) for GLD ETF and Gold (GC) iNAV Volatility. Bayesian VAR impulse responses exhibiting the most pronounced asymmetries: iNAV shocks create large and persistent responses in ETF volatility that decay smoothly, while ETF shocks generate negligible responses in iNAV, providing strong dynamic evidence for unidirectional transmission in gold markets.}
\label{ch2:fig:irf2}
\end{figure}
\end{landscape}

\begin{landscape}
\begin{figure}[t]
\includegraphics[width=16cm,trim=0 0 0 22,clip]{silver__slv_si__irf.pdf}
\centering
\caption{Impulse Response Functions (IRF) for SLV ETF and Silver (SI) iNAV Volatility. Bayesian VAR impulse responses preserving the gold market's asymmetric structure but with qualitatively richer adjustment dynamics and greater variability, reflecting silver's dual function as both an industrial and a precious metal.}
\label{ch2:fig:irf3}
\end{figure}
\end{landscape}

\begin{landscape}
\begin{figure}[t]
\includegraphics[width=16cm,trim=0 0 0 22,clip]{gas__ung_ng__irf.pdf}
\centering
\caption{Impulse Response Functions (IRF) for UNG ETF and Natural Gas (NG) iNAV Volatility. Bayesian VAR impulse responses exhibiting the most elaborate structures with large responses in both directions, delayed peaks, and periodic behavior, substantiating bidirectional transmission involving numerous channels and horizons in natural gas markets.}
\label{ch2:fig:irf4}
\end{figure}
\end{landscape}
