% ============================================================================
\section{Conclusion}
\label{sec:conclusion}
% ============================================================================

This paper has measured the transmission of realized volatility across equity index futures, major exchange rates, gold and crude oil futures, the VIX and the two largest cryptocurrencies, using daily realized volatilities built from 5-minute bars and the generalized variance decomposition of a VAR estimated on the 2{,}514 trading days common to all ten series between March 2016 and March 2026. Cross-asset shocks account for 54.8\% of forecast-error variance. The E-mini S\&P~500 and Nasdaq~100 futures are the only robust net transmitters; the realized volatility of the VIX, crude oil and sterling are robust net receivers; and the net positions of the euro, the yen, gold, bitcoin and ether cannot be distinguished from zero over the decade. These conclusions hold across lag orders, forecast horizons, the treatment of weekend crypto variance, and the inclusion or exclusion of the VIX and of the cryptocurrencies.

The cryptocurrencies form a tightly linked pair whose exposure to the traditional system has grown from under 10\% of forecast-error variance before 2020 to between 20\% and 46\% since, with the net flow running from U.S. equities to crypto: bitcoin and ether are significant net receivers in the spot-ETF period, the previous day's U.S.-session volatility of equity futures predicts bitcoin's Asian-session volatility, and neither bitcoin's overnight nor its weekend volatility predicts the U.S.-session volatility of equity futures. Total connectedness rose during the COVID-19 crash, when exchange-rate volatility became the common factor, and reached its highest level of the sample in 2025. Intraday, equity and VIX volatility are concentrated in the U.S. cash session while bitcoin's volatility is nearly uniform across the day and the week.

The revision of this paper has also been an exercise in the sensitivity of connectedness measures to data construction. Aligning 24/7 and exchange-traded series on a common trading calendar, rather than forward-filling the latter over weekends, changed the total index by five percentage points, the net spillover of equity futures by fifteen, and the apparent isolation of the crypto block from near-complete to partial; attaching bootstrap intervals to regime estimates showed that several sign changes reported in the earlier version, and in parts of the literature, are within sampling error; and converting exchange time stamps to UTC relocated the intraday volatility peaks from the European to the U.S. session. We regard these corrections as part of the paper's contribution.

Three extensions appear most promising. A frequency decomposition of connectedness \citep{Barunik2018} would show whether the equity-to-crypto transmission documented here operates at short or long horizons. A time-varying-parameter VAR \citep{Antonakakis2020} or a shrinkage estimator would recover time variation in the hierarchy with fewer effective parameters than rolling windows and would allow a formal test of the 2020 break in crypto integration. And jump-robust, single-exchange realized measures for the cryptocurrencies, together with the removal of futures roll returns, would tighten the measurement side on which the whole analysis rests.