## Pricing Geopolitical Risk: Real-Time Evidence from Oil and Gas Markets — Online Annex 1.1

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### Part I. Data, Sources, and Transformations
- Frequency and working days:
  - Daily data on US working days only for oil and Dutch working days only for TTF.
- Oil price series and transformations:
  - One-month oil price: weighted average of front-month Brent settlement price from Refinitiv (LCOc1) and North Sea Dated Brent from Argus; transformation ensures contract maturity is always one month ahead; percentage changes expressed as 100*log(p_one-month_t).
  - 13-month oil futures price: Refinitiv (LCOc13), transformed as 100*log(p_13month_t).
  - Notable market facts:
    - Front-month experienced a drop of about $17 on April 1st 2026 as the reference period moved from May to June.
    - On January 29, 2016 a change was introduced in the expiry calendar of Brent contracts producing prices that thereafter refer to deliveries roughly one month further ahead compared to prices until then.
- TTF gas price seasonal adjustment procedure (Bloomberg: TZT1 Comdty, TZT2 Comdty, TZT13 Comdty, TZT14 Comdty):
  - Transform TTF prices in logarithms and multiply by 100.
  - Compute roll gaps as log-price difference between 2-month ahead futures (TZT2) and front-month (TZT1).
  - Adjusted log-price = observed log-price + cumulation of future roll gaps.
  - Percentage price change = difference of adjusted log-price series.
  - (Log)-back-adjusted price series computed forward adding continuous percentage price change to ln(original price).
  - Resulting (log)-back-adjusted TTF price series in levels is seasonally adjusted with STL.
  - Procedure repeated for front-month and 13-month ahead futures.
- Financial and news measures:
  - Cumulated equity daily returns: 1-year rolling window on daily returns of MSCI indices.
    - For oil: MSCI All country World Index (ACWI) from Refinitiv.
    - For gas: MSCI Europe index from Bloomberg (MXEU Index).
  - 7-day moving average of the GPRT index obtained from https://www.matteoiacoviello.com/gpr.htm (US working days for oil SVAR; Dutch working days for gas SVAR).
- Instrumental variables and demand/supply proxies:
  - Oil Forward Demand proxy IV:
    - Selects days with large change in VIX, OVX, GC1 (gold), and a large change in front-month oil price of the opposite direction (below 10th percentile or above 90th percentile).
    - Identifies 25 events in the sample.
    - Forward Demand IV takes the value of the VIX on selected days and 0 otherwise.
    - Procedure from Gazzani and others (2024).
  - TTF Current Demand proxy IV:
    - Based on daily mean temperature forecasts from “CFSV2: NCEP Climate Forecast System Version 2” (Saha and others 2014).
    - Aggregated using population weights from “LandScan Global Population Dataset” (Sims and others (2023)).
    - Total degree days (TDD) computed as sum of HDD and CDD using threshold 18°C (65°F).
    - Aggregated European TDD uses one-year lagged annual gas consumption from “2025 Energy Institute Statistical Review of World Energy” (Energy Institute 2025).
    - Temperature anomalies = aggregated European TDD minus average TDD for same calendar day over previous five years.
- Sample construction for local projections:
  - Oil shock analysis sample restricted to advanced-economy net oil importers: Germany, Spain, France, Italy, Japan, Korea, and the United States (classification based on latest annual crude oil trade from EIA).
  - LNG shock analysis sample restricted to five major European economies: Germany, Spain, France, Italy, and the United Kingdom.

### Part II. Structural Vector Autoregression — Model and Identification
- Model specification:
  - Structural form: A0 D_t = p + A1 D_{t-1} + ... + A_p D_{t-p} + u_t, with u_t ~ i.i.d. N(0,1); p = 4 lags.
  - D_t is a vector of four variables: adjusted front-month, futures, equity index returns, and GPRT.
  - Reduced-form: D_t = A0^{-1} p + B1 D_{t-1} + ... + B_p D_{t-p} + e_t, with e_t ~ i.i.d. N(0, Σ) and Σ = (A0' A0)^{-1}.
- Structural shocks identified (for oil and gas separately):
  - (i) Forward-looking demand (FD):
    - Oil: identified using proxy IV (proxy-SVAR).
    - Gas: forward-looking demand identified through positive impact on futures and equities.
  - (ii) Current demand (CD):
    - Imposes positive impact on front-month and futures and stronger impact on front-month relative to futures (backwardation); positive correlation with equities (for oil).
    - For gas, current demand is identified with a weather-based proxy IV.
  - (iii) Current supply:
    - Identified by a negative correlation between front-month oil and equities (for oil).
  - (iv) Geopolitical supply risk (GSR) or forward-looking supply:
    - Identified by imposing a positive correlation between 7-day moving average of GPRT and front-month prices while leaving futures and equities responses unrestricted.
- Identification restrictions:
  - Proxy IVs used for FD or CD as described; (S) denotes stronger and (W) denotes weaker response (relative magnitude restriction).
  - (Schematic mapping across variables and shocks preserved as in source.)

### Part III. Estimation Methodology
- Software and algorithm:
  - Estimation uses ECB BEAR toolbox (Dieppe and others, 2016).
  - Metropolis-within-Gibbs algorithm of Caldara and Herbst (2019) as implemented in BEAR.
- Priors and parametrization:
  - Reduced-form VAR coefficients prior: Normal-Wishart, B|Σ ~ N(b0, Σ ⊗ Φ0), Σ ~ IW(S0, α0).
  - Φ0 diagonal entries for lag ℓ of variable j equal 1/σ_j^2 * (λ1 / ℓ^{λ3}).
  - Parameter values: b0 = 0.8 for each variable’s own first lag and 0 otherwise; λ1 = 1; λ3 = 1.
  - σ_j^2 pre-computed as OLS residual variances of univariate AR(p) regressions.
  - S0 diagonal elements from individual AR regressions.
  - α0 = n + 2, where n is number of variables.
  - Measurement equation priors (following Caldara and Herbst (2019)): β ~ N(0,1); measurement error standard deviation σ_v^2 ~ IW(s1, s2) with s1 = 2 and s2 = 0.02 for oil.
  - For natural gas: use BEAR high relevance prior option imposing that half of variation in proxy can be attributed to measurement error.
- Implementation details:
  - Proxy IV pins down the column b1 corresponding to the FD (or CD) shock; sign and relative magnitude restrictions enter as rotation matrices tested at each draw.
  - Simulation: 2000 iterations with first 200 used as burn-in.

### Part IV. Macroeconomic Impact of Energy Price Shocks: Local Projections
- Method:
  - Local projection method of Jordà (2005).
  - Separate panel regression for each horizon h = 0, ..., 24.
  - Oil and LNG shocks and each of the four shock types entered separately.
- CPI specification:
  - Dependent variable: cumulative change in logarithm of price level from pre-shock month t−1 to horizon t+h, expressed as 100*(log(CPI_{i,t+h}) − log(CPI_{i,t−1})).
  - Regression for each horizon h:
    - 100*(log(CPI_{i,t+h}) − log(CPI_{i,t−1})) = α_i + β_h Shock_{t} + θ_h Controls_{t} + δ_h (Shock_t × Controls_t) + Σ_{l=1}^{12} φ_{l,h} π_{i,t−l} + ε_{i,t+h}.
  - Controls include COVID-19 dummy equal to one between March 2020 and June 2020 and zero otherwise, and interaction between the dummy and the shock variable.
  - Outside March–June 2020, β_h measures impact of oil or LNG shocks on cumulative percentage change in CPI level at horizon h relative to CPI_{i,t−1}; during March–June 2020 the corresponding coefficient is β_h + δ_h.
  - Standard errors clustered at the country level.
- Unemployment specification:
  - Dependent variable: unemployment rate in levels at horizon t+h.
  - Regression for each horizon h:
    - u_{i,t+h} = α_i + β_h Shock_t + θ_h Controls_t + δ_h (Shock_t × Controls_t) + Σ_{l=1}^{12} φ_{l,h} u_{i,t−l} + ε_{i,t+h}.
  - Controls comprise twelve lags of unemployment; standard errors clustered at the country level.
  - Outside March–June 2020, β_h measures the unemployment response to the specified shock.
- Figures and horizons:
  - Online Annex Figure 1.1.1 shows local projection estimates of unemployment responses to oil shocks in advanced oil-importing economies for horizons up to 24 months, with separate panels including Forward-Looking Demand and other shocks.

### Key numerical and sample details (preserved exactly)
- p = 4 lags in SVAR.
- 1-year rolling window for cumulated equity daily returns.
- 7-day moving average used for GPRT index.
- Forward Demand IV event selection thresholds: below 10th percentile or above 90th percentile.
- Forward Demand IV identifies 25 events in the sample.
- Temperature threshold for TDD: 18°C (65°F).
- Local projection horizons: h = 0, ..., 24.
- Simulation: 2000 iterations with first 200 used as burn-in.
- CPI regression includes Σ_{l=1}^{12} lags; unemployment regression includes Σ_{l=1}^{12} lags.
- COVID-19 dummy equal to one between March 2020 and June 2020 and zero otherwise.
- Oil shock sample (advanced-economy net oil importers): Germany, Spain, France, Italy, Japan, Korea, and the United States.
- LNG shock sample: Germany, Spain, France, Italy, and the United Kingdom.

### Part IV (Section 2): Effect of Oil Shocks on Unemployment — Dynamic Response
- Sample period for pre-ChatGPT release analysis: June 2007–October 2022.
- The sequence {훽훽_h}_h=0^24 traces the baseline dynamic response over a two-year horizon.
- During March–June 2020, the corresponding shock coefficient is 훽훽_h + 휹휹_h.
- Estimation specification features:
  - Country fixed effects absorb time-invariant cross-country heterogeneity.
  - Twelve-monthly lags capture persistence in inflation and unemployment.
- Graphic numeric axis values presented in the figure (preserved exactly):
  - CurrentDemand: –0.04, 0.00, 0.04, 0.08, 0.12
  - c. Supply: –0.07, –0.04, 0.00, 0.04, 0.07
  - d. GeopoliticalSupply Risk: (Percent change; monthly horizon on the x-axis)
  - X-axis ticks: 0 4 8 12 16 20 24

*International Monetary Fund | October 2026*

### Section 1

### Pricing Geopolitical Risk: Real-Time Evidence from Oil and Gas Markets — Online Annex 1.1 (Section 1)

### Part I. Data, Sources, and Transformations
- Daily data on US working days only for oil and Dutch working days only for TTF. Variables:
  - One-month oil price: weighted average of front-month Brent settlement price from Refinitiv (LCOc1) and North Sea Dated Brent from Argus. Transformation ensures contract maturity is always one month ahead. Percentage changes expressed as 100*log(p_one-month_t).
  - Seasonally adjusted TTF prices: sourced from Bloomberg (TZT1 Comdty, TZT2 Comdty, TZT13 Comdty, TZT14 Comdty). Procedure:
    - Transform TTF prices in logarithms and multiply by 100.
    - Compute roll gaps as log-price difference between 2-month ahead futures (TZT2) and front-month (TZT1).
    - Adjusted log-price = observed log-price + cumulation of future roll gaps.
    - Percentage price change = difference of adjusted log-price series.
    - (Log)-back-adjusted price series computed forward adding continuous percentage price change to ln(original price).
    - Resulting (log)-back-adjusted TTF price series in levels is seasonally adjusted with STL.
    - Procedure repeated for front-month and 13-month ahead futures.
  - 13-month oil futures price: Refinitiv (LCOc13), transformed as 100*log(p_13month_t).
  - Cumulated equity daily returns: 1-year rolling window on daily returns of MSCI indices. For oil: MSCI All country World Index (ACWI) from Refinitiv. For gas: MSCI Europe index from Bloomberg (MXEU Index).
  - 7-day moving average of the GPRT index obtained from https://www.matteoiacoviello.com/gpr.htm (US working days for oil SVAR; Dutch working days for gas SVAR).
  - Oil Forward Demand proxy IV: selects days with large change in VIX, OVX, GC1 (gold), and a large change in front-month oil price of the opposite direction (below 10th percentile or above 90th percentile). Identifies 25 events in the sample. Forward Demand IV takes the value of the VIX on selected days and 0 otherwise. Procedure from Gazzani and others (2024).
  - TTF Current Demand proxy IV: based on daily mean temperature forecasts from “CFSV2: NCEP Climate Forecast System Version 2” (Saha and others 2014), aggregated using population weights from “LandScan Global Population Dataset” (Sims and others (2023)). Total degree days (TDD) computed as sum of HDD and CDD using threshold 18°C (65°F); aggregated European TDD uses one-year lagged annual gas consumption from “2025 Energy Institute Statistical Review of World Energy” (Energy Institute 2025). Temperature anomalies = aggregated European TDD minus average TDD for same calendar day over previous five years.
- Notable data/market facts preserved from source:
  - Front-month experienced a drop of about $17 on April 1st 2026 as the reference period moved from May to June.
  - On January 29, 2016 a change was introduced in the expiry calendar of Brent contracts producing prices that thereafter refer to deliveries roughly one month further ahead compared to prices until then.
- Sample construction for local projections:
  - Oil shock analysis: sample restricted to advanced-economy net oil importers (Germany, Spain, France, Italy, Japan, Korea, and the United States), classification based on latest annual crude oil trade from EIA.
  - LNG shock analysis: sample restricted to five major European economies: Germany, Spain, France, Italy, and the United Kingdom.

### Part II. Structural Vector Autoregression — Model and Identification
- Structural form (compact description): A0 D_t = p + A1 D_{t-1} + ... + A_p D_{t-p} + u_t, with u_t ~ i.i.d. N(0,1). p = 4 lags. D_t is a vector of four variables: adjusted front-month, futures, equity index returns, and GPRT.
- Reduced-form: D_t = A0^{-1} p + B1 D_{t-1} + ... + B_p D_{t-p} + e_t, with e_t ~ i.i.d. N(0, Σ) and Σ = (A0' A0)^{-1}.
- Four structural shocks identified for oil and gas separately:
  - (i) Forward-looking demand (FD): for oil, identified using proxy IV (proxy-SVAR). For gas, forward-looking demand identified through positive impact on futures and equities.
  - (ii) Current demand (CD): imposes positive impact on front-month and futures and stronger impact on front-month relative to futures (backwardation); positive correlation with equities (for oil). For gas, current demand is identified with a weather-based proxy IV.
  - (iii) Current supply: identified by a negative correlation between front-month oil and equities (for oil).
  - (iv) Geopolitical supply risk (GSR) or forward-looking supply: identified by imposing a positive correlation between 7-day moving average of GPRT and front-month prices while leaving futures and equities responses unrestricted.
- Identification restrictions summarized (structure preserved): proxy IVs used for FD or CD as described; (S) denotes stronger and (W) denotes weaker response (relative magnitude restriction). (See Online Annex Table 1.1.2 for mapping across variables and shocks in oil and gas SVARs.)
- Economic interpretation examples preserved from source:
  - GSR includes stockpiling and fears of future supply disruptions (examples: Ukraine-Russia War during 2022; Iran-Israel Twelve-Day War in 2025; possibility of SoH closure in 2026 Middle East War context).

### Part III. Estimation Methodology
- Estimation uses ECB BEAR toolbox (Dieppe and others, 2016).
- Priors and parametrization:
  - Reduced-form VAR coefficients prior: Normal-Wishart, B|Σ ~ N(b0, Σ ⊗ Φ0), Σ ~ IW(S0, α0).
  - Φ0 diagonal entries for lag ℓ of variable j equal 1/σ_j^2 * (λ1 / ℓ^{λ3}). Parameter values: b0 = 0.8 for each variable’s own first lag and 0 otherwise; λ1 = 1; λ3 = 1. σ_j^2 pre-computed as OLS residual variances of univariate AR(p) regressions. S0 diagonal elements from individual AR regressions. α0 = n + 2, where n is number of variables.
  - Measurement equation priors (following Caldara and Herbst (2019)): β ~ N(0,1); measurement error standard deviation σ_v^2 ~ IW(s1, s2) with s1 = 2 and s2 = 0.02 for oil.
  - For natural gas: use BEAR high relevance prior option imposing that half of variation in proxy can be attributed to measurement error.
- Algorithm and implementation:
  - Metropolis-within-Gibbs algorithm of Caldara and Herbst (2019) as implemented in BEAR.
  - Proxy IV pins down the column b1 corresponding to the FD (or CD) shock; sign and relative magnitude restrictions enter as rotation matrices tested at each draw.
  - Simulation: 2000 iterations with first 200 used as burn-in.

### Part IV. Macroeconomic Impact of Energy Price Shocks: Local Projections
- Method: Local projection method of Jordà (2005). Separate panel regression for each horizon h = 0, ..., 24. Oil and LNG shocks and each of the four shock types entered separately.
- Consumer Price Index (CPI) specification:
  - Dependent variable: cumulative change in logarithm of price level from pre-shock month t−1 to horizon t+h, expressed as 100*(log(CPI_{i,t+h}) − log(CPI_{i,t−1})).
  - Regression for each horizon h:
    - 100*(log(CPI_{i,t+h}) − log(CPI_{i,t−1})) = α_i + β_h Shock_{t} + θ_h Controls_{t} + δ_h (Shock_t × Controls_t) + Σ_{l=1}^{12} φ_{l,h} π_{i,t−l} + ε_{i,t+h}.
    - Controls include COVID-19 dummy equal to one between March 2020 and June 2020 and zero otherwise, and interaction between the dummy and the shock variable.
    - Interpretation: outside COVID-19 window, β_h measures impact of oil or LNG shocks on cumulative percentage change in CPI level at horizon h relative to CPI_{i,t−1}. During March–June 2020 the corresponding coefficient is β_h + δ_h.
  - Standard errors clustered at the country level.
- Unemployment rate specification:
  - Dependent variable: unemployment rate in levels at horizon t+h.
  - Regression for each horizon h:
    - u_{i,t+h} = α_i + β_h Shock_t + θ_h Controls_t + δ_h (Shock_t × Controls_t) + Σ_{l=1}^{12} φ_{l,h} u_{i,t−l} + ε_{i,t+h}.
    - Controls comprise twelve lags of unemployment; standard errors clustered at the country level.
    - Outside the COVID-19 window, β_h measures the unemployment response to the specified shock.
- Figure referenced: Online Annex Figure 1.1.1 shows local projection estimates of unemployment responses to oil shocks in advanced oil-importing economies for horizons up to 24 months, with panels for Forward-Looking Demand and other shocks (figure axes labels and sample note preserved).

*International Monetary Fund | October 2026*

### Section 2

### ch1onlineannex - Section 2

### Effect of Oil Shocks on Unemployment (Dynamic Response)
- Figure 1.1.1 presents the effect of oil shocks on the unemployment rate for the pre-ChatGPT release (June 2007-October 2022).
- The sequence {훽훽_h}_h=0^24 traces the baseline dynamic response over a two-year horizon.
- During March-June 2020, the corresponding shock coefficient is 훽훽_h + 휹휹_h.
- Country fixed effects absorb time-invariant cross-country heterogeneity; twelve-monthly lags account for persistence in inflation and unemployment.
- Graphic numeric axis values shown:
  - CurrentDemand: –0.04, 0.00, 0.04, 0.08, 0.12
  - c. Supply: –0.07, –0.04, 0.00, 0.04, 0.07
  - d. GeopoliticalSupply Risk: (Percent change; monthly horizon on the x-axis)
  - X-axis ticks: 0 4 8 12 16 20 24

### Methodology and Estimation
- Estimation uses local projections: Jordà, Oscar. 2005. “Estimation and Inference of Impulse Responses by Local Projections.” American Economic Review 95 (1): 161–182.
- The analysis reports percentage-point effect of the shock on unemployment at horizon h relative to the counterfactual unemployment path absent shock.
- Specifications include country fixed effects and twelve-monthly lags to capture persistence.

### Time periods and sample
- Pre-ChatGPT release sample period: June 2007–October 2022.
- Special notation for March–June 2020 shock period.

### References cited in this section (selected items preserved exactly as in source)
- Caldara, Dario, and Edward Herbst. 2019. “Monetary Policy, Real Activity, and Credit Spreads: Evidence from Bayesian Proxy SVARs.” American Economic Journal: Macroeconomics 11(1): 157-192
- Dieppe, Alistair, Bjorn van Roye, and Romain Legrand. 2016. “The BEAR toolbox.” ECB Working Paper Series No. 1934.
- Energy Institute. 2025. Statistical Review of World Energy, 74th edition.
- Fama, Edward. 1990. “Stock Returns, Expected Returns, and Real Activity.” The Journal of Finance 45(4): 1089-1108
- Gazzani, Andrea, Fabrizio Venditti, and Giovanni Veronese. 2024. “Oil Price Shocks in Real Time.” Journal of Monetary Economics 144: 103547.
- Kilian, Lutz, and Cheolbeom Park. 2009. “The Impact of Oil Price Shocks on the U.S. Stock Market.” International Economic Review 50(4): 1267–1287.
- Kilian, Lutz, Michael Plante, and Alexander W. Richter. 2026. “Geopolitical Oil Price Risk and Economic Fluctuations.” Federal Reserve Bank of Dallas, Working Paper No. 2403.
- Ma, Christopher, Jeffrey M. Mercer, and Matthew A. Walker. 1992. “Rolling Over Future Contracts: A Note”. The Journal of Futures Markets 12(2): 203-217.
- Pinchetti, Marco. 2026. “Geopolitical Risk and Inflation: The Role of Energy Markets.” Mimeo. July.
- Ready, Robert C. 2018. “Oil prices and the stock market.” Review of Finance 22(1): 155–176.
- Saha, Suranjana, Shrinivas Moorthi, Xingren Wu, Jiande Wang, Sughir Nadiga, Patrick Tripp, David Behringer, Yu-Tai Hou, Hui-ya Chuang, Mark Iredell, Michael Ek, Jesse Meng, Rongqian Yang, Malaquias Peña Mendez, Huug van den Dool, Qin Zhang, Wanqiu Wang, Mingyue Chen, and Emily Becker. 2014. “The NCEP Climate Forecast System Version 2.” Journal of Climate 27(6): 2185-2208.
- Sims, Kelly, Andrew Reith, Eddie Bright, Jason Kaufman, Joe Pyle, Justin Epting, Jack Gonzales, Daniel Adams, Eric Powell, Marie Urban, and Amy Rose. (2023). LandScan Global 2022 [Data set]. Oak Ridge National Laboratory. https://doi.org/10.48690/1529167

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_Source: https://www.imf.org/-/media/files/publications/weo/2026/october/english/ch1onlineannex.pdf_