Measuring Financial Connectedness & Spillovers
How do shocks propagate across financial markets? This lab introduces the Diebold-Yilmaz connectedness framework: a VAR-based decomposition that quantifies who transmits risk, who absorbs it, and how the network tightens during crises.
Durée indicative : 40–50 min (10 min théorie, 10 min données, 15 min exercice connectedness, 10 min réseau, 5 min export).
The Connectedness Framework
The Diebold-Yilmaz (DY) connectedness framework, introduced across three landmark papers (2009, 2012, 2014), provides a unified approach to measuring spillovers between financial variables. The method builds on Generalized Variance Decompositions from Vector Autoregressions (VAR), following the identification-free approach of Pesaran & Shin (1998).
The core idea: estimate a VAR for a system of N financial variables, then compute the share of each variable's forecast error variance that is attributable to shocks originating in other variables. These shares, organized in a matrix, reveal the direction, intensity, and network structure of cross-market spillovers.
"In a globalizing world it is important to understand the nature and degree of connectedness of a system. [...] We characterize connectedness based on variance decomposition networks."Diebold & Yilmaz (2014), Journal of Econometrics
Step 1: Estimate a VAR
Fit a VAR(p) model to a system of N variables. The generalized impulse response (Pesaran-Shin) approach avoids the ordering dependence of Cholesky decompositions, making results robust to variable ordering.
Step 2: Variance Decomposition
Compute the H-step-ahead generalized FEVD. The element Cij is the share of the H-step forecast error variance of variable i attributable to shocks from variable j. Rows are normalized to sum to 100%.
Key Connectedness Measures
Total Connectedness Index (TCI)
Average off-diagonal FEVD share. Captures system-wide interconnectedness. Rises sharply during crises.
FROM Connectedness
Row sum of off-diagonal elements: how much of variable i's forecast error variance comes from shocks in all other variables.
TO Connectedness
Column sum of off-diagonal elements: how much variable j contributes to forecast error variance of all other variables.
NET Connectedness
TO minus FROM. Positive = net transmitter of shocks. Negative = net receiver. Identifies systemic risk sources.
References
- Diebold, F.X. & Yilmaz, K. (2009). "Measuring Financial Asset Return and Volatility Spillovers, with Application to Global Equity Markets." Economic Journal, 119(534), 158-171.
- Diebold, F.X. & Yilmaz, K. (2012). "Better to Give than to Receive: Predictive Directional Measurement of Volatility Spillovers." International Journal of Forecasting, 28(1), 57-66.
- Diebold, F.X. & Yilmaz, K. (2014). "On the Network Topology of Variance Decompositions: Measuring the Connectedness of Financial Firms." Journal of Econometrics, 182(1), 119-134.
- Pesaran, M.H. & Shin, Y. (1998). "Generalized Impulse Response Analysis in Linear Multivariate Models." Economics Letters, 58(1), 17-29.
Data Exploration
We work with monthly data on six key macro-financial variables that capture distinct channels of risk transmission: equity volatility, exchange rates, bond yields, commodities, safe havens, and emerging market credit.
VIX
S&P 500 implied volatility. Fear gauge.
EUR/USD Vol
3-month implied volatility on EUR/USD.
US 10Y
Treasury yield. Safe-haven benchmark.
Oil (WTI)
Crude oil price, USD/barrel.
Gold
Safe-haven asset. USD/oz.
EMBI Spread
EM sovereign spread. Credit risk proxy.
Normalized Time Series (z-scores)
Click variable chips to toggle visibility. All series standardized to facilitate comparison.
Full-Sample Correlation Matrix (2006-2024)
Color intensity encodes correlation magnitude. Blue = positive, red = negative.
Explore Connectedness Across Regimes
The connectedness matrix below shows H=10 step-ahead generalized FEVD results for a VAR(2) estimated on the six variables. Select a period to see how the structure of spillovers changes between tranquil and crisis times.
Connectedness Matrix (2022-2023)
Diagonal = own variance share. Off-diagonal = cross-variable spillovers. FROM = row total (excl. own). TO = column total (excl. own).
Rolling Total Connectedness Index
60-month rolling window. Grey bands mark major crisis episodes.
Directional Connectedness: NET Transmitters vs Receivers
NET = TO - FROM. Positive bars = net shock transmitters. Negative = net receivers. Select period above to update.
Comprehension Check
Q1. During the GFC, which variable is the biggest NET transmitter of shocks?
Q2. How does the Total Connectedness Index behave during crises?
Q3. During the post-Ukraine period (2022-2023), which pair shows the strongest bilateral connectedness?
Q4. What does a negative NET connectedness value for Gold typically indicate?
Connectedness Network
The network below arranges the six variables as nodes. Edge thickness is proportional to the pairwise connectedness (bidirectional average). Node color indicates whether the variable is a net transmitter (red) or net receiver (blue) of shocks in the selected period. Node size reflects the magnitude of net connectedness.
Switch between periods to observe how the network tightens during crises: edges thicken, the system becomes more densely connected, and shock transmission roles shift.
Cross-Period Comparison
How key metrics shift across regimes.
| Metric | Pre-GFC | GFC | Post-Ukraine |
|---|
What Have We Learned?
1. Connectedness is time-varying and regime-dependent. The Total Connectedness Index rises from roughly 38% in tranquil periods to above 68% during crises. Financial markets become substantially more interconnected when stress materializes, reflecting contagion channels, portfolio rebalancing, and flight-to-quality flows.
2. VIX is the dominant net transmitter. Equity volatility consistently transmits the most shocks to other variables, especially during the GFC when VIX net connectedness peaked. This confirms VIX as a barometer of systemic risk propagation, not just domestic equity fear.
3. Gold and US Treasuries act as shock absorbers. Both show negative net connectedness during crisis periods, absorbing shocks rather than propagating them. This is the quantitative fingerprint of the safe-haven effect.
4. The post-2022 regime differs from the GFC. Post-Ukraine connectedness is elevated but structurally different: oil becomes a stronger transmitter (energy shock channel), and EMBI spreads show heightened sensitivity to VIX, reflecting the commodity-EM nexus.
Comparison with Published Results
Our findings align closely with the canonical results from Diebold & Yilmaz (2012): TCI spikes during the GFC (their estimate: ~65% for equity markets), directional measures identify equity volatility as the dominant transmitter, and the network topology tightens during stress. The extension to 2022-2024 shows that the Ukraine shock produced a connectedness spike comparable in magnitude to the GFC, consistent with recent applications of the framework to geopolitical risk (Caldara & Iacoviello, 2022).
Your Score
Export & Resources
ConnectednessApproach and vars
packages to replicate the analysis with actual data from FRED, Yahoo Finance, and J.P. Morgan.
References
- Diebold, F.X. & Yilmaz, K. (2009). "Measuring Financial Asset Return and Volatility Spillovers, with Application to Global Equity Markets." Economic Journal, 119(534), 158-171.
- Diebold, F.X. & Yilmaz, K. (2012). "Better to Give than to Receive: Predictive Directional Measurement of Volatility Spillovers." International Journal of Forecasting, 28(1), 57-66.
- Diebold, F.X. & Yilmaz, K. (2014). "On the Network Topology of Variance Decompositions: Measuring the Connectedness of Financial Firms." Journal of Econometrics, 182(1), 119-134.
- Pesaran, M.H. & Shin, Y. (1998). "Generalized Impulse Response Analysis in Linear Multivariate Models." Economics Letters, 58(1), 17-29.