spb/wp6_uqo

1% ============================================================================2\section{Discussion}3\label{sec:discussion}4% ============================================================================56\subsection{Addressing the Research Questions}78\paragraph{RQ1: Intraday volatility propagation.} Our analysis reveals a clear hierarchical structure in cross-asset volatility propagation. U.S.\ equity index futures serve as the primary volatility transmitters, with combined net spillovers exceeding $+46\%$. Volatility propagates outward from equities to FX (particularly EURUSD), commodities, and the VIX. Crypto markets remain largely insulated, with own-shock contributions exceeding 77\%. The total spillover index of 55.44\% underscores the limitations of single-asset volatility models.910\paragraph{RQ2: Regime dependence.} The magnitude, direction, and speed of volatility transmission vary dramatically across regimes. Three patterns emerge: (i)~in tranquil periods, equity futures dominate (ES net: $+76.4\%$ pre-COVID); (ii)~during acute crises, safe-haven currencies assume the transmitter role (USDJPY: $+60.3\%$ during COVID); (iii)~during macro-driven regimes, transmission becomes more distributed (EURUSD: $+9.5\%$, BTC: $+7.9\%$ during 2022). The TSI itself is less responsive to regime shifts (64.7\%--66.7\%) than the directional composition, suggesting that ``who transmits to whom'' is more informative than ``how much total transmission occurs.''1112\paragraph{RQ3: Volatility hierarchy and crypto integration.} The full-sample hierarchy is: ES~($+26.8$) $>$ NQ~($+19.7$) $>$ BTC~($+1.2$) $>$ EURUSD~($+0.4$) $>$ ETH~($-1.0$) $>$ GC~($-2.9$) $>$ USDJPY~($-5.0$) $>$ CL~($-7.2$) $>$ GBPUSD~($-8.7$) $>$ VIX~($-23.4$). BTC's transition from neutral/receiver to significant transmitter ($+7.9\%$ during rate hikes) represents a structural shift, consistent with institutional adoption and spot Bitcoin ETF approvals.1314\paragraph{RQ4: Systemic risk indicator.} The rolling TSI demonstrates potential as a systemic risk monitor: (i)~it rises \textit{before} major events (the 200-day window captures gradual dependency buildups); (ii)~the maximum (81.55\%, February 2018) precedes the Volmageddon episode; (iii)~it correctly identifies the 2022 rate-hiking cycle as elevated systemic risk. However, the rolling window introduces smoothing that can delay detection of rapid shifts.1516\paragraph{RQ5: Trading session differences.} Equity futures and VIX concentrate volatility during European and U.S.\ hours, with the European session generating the highest volatility for both ES (0.060\%) and NQ (0.073\%). Bitcoin's near-uniform volatility across sessions (0.245\%--0.266\%) reflects its 24/7 market structure. Granger causality confirms the primacy of equity futures in driving VIX ($F = 19.86$) and the causal independence of Bitcoin.1718\subsection{Implications for Portfolio Construction and Risk Management}1920Our findings carry several practical implications. First, the documented spillover asymmetries complicate cross-asset hedging: VIX instruments respond to equity shocks rather than providing independent signals. Second, the growing crypto--traditional integration during the 2022 rate-hiking period suggests diminishing diversification benefits of crypto allocation precisely when diversification is most needed. Third, the session-dependent nature of volatility transmission implies that risk limits could be optimized by trading session, with tighter controls during the European--U.S.\ overlap.2122\subsection{Limitations}2324Several limitations merit acknowledgment. First, the realized volatility measure based on 5-minute returns may be affected by microstructure noise during illiquid periods. Second, the VAR(4) model imposes a linear structure that may not fully capture nonlinear and asymmetric spillovers during extreme events. Third, the 200-day rolling window involves a trade-off between responsiveness and estimation precision. Fourth, the Granger causality analysis uses daily realized volatility without session-specific splitting, reflecting full-sample relationships. Fifth, the selection of 10 assets, while covering the major classes, excludes potentially important instruments such as emerging market currencies, agricultural commodities, and smaller cryptocurrencies.25