By Davide Brignone, Satyam Goel, Simon Lloyd, Giulia Mantoan, Nades Raviraj and Andrea Renzetti.
Like all forecasts, scenarios are simplifications of reality — one possible path among many. Without a sense of the overall risks around the outlook, it can be hard to judge how plausible or extreme a scenario is. In this sense, predictive densities – probability distributions over possible outcomes – complement scenarios. Examples include fan charts and other statistical risk-forecasting models, such as the ‘outlook-at-risk’ framework pioneered by staff at the Federal Reserve Bank of New York and further developed by Bank staff.
To bridge this gap, Bank staff have been adapting the ‘scenario synthesis’ approach developed by Adrian et al (2025). This article summarises insights from that work, by retrospectively applying the approach to Scenarios A, B and C – which demonstrate how different paths for global energy prices, and possible second-round effects on domestic price and wage-setting, could affect the UK economy – from the April 2026 MPR.
What the scenario synthesis does.
The scenario synthesis is a statistical framework connecting density forecasts to narrative scenarios. It can be used to assess how well a set of scenarios collectively captures a given set of macroeconomic risks. It can also highlight cases where scenarios are statistically indistinguishable, or flag gaps where estimated risks are not covered by any scenario. In that way, the approach can be used to inform scenario design more rigorously.
The approach, summarised visually in Figure 1, combines two inputs: (i) a reference distribution that reflects the overall (‘unconditional’) risk outlook, which can be drawn from a range of sources (surveys, statistical risk-forecasting models, or financial markets); and (ii) a set of projections and scenarios (which can include a ‘central’ outlook) expressed as density forecasts, each reflecting a different ‘conditional’ view of the world based on an alternative set of assumptions.footnote [1]
Figure 1: Summary of the scenario synthesis approach
In turn, it delivers two outputs: (i) implied scenario weights, which quantify the contribution of each scenario in explaining the reference distribution; (ii) a predictive synthesis distribution, which is a weighted mixture of scenario densities that most closely matches the reference distribution.
Both outputs are valuable for scenario design. Scenario weights can indicate the statistical relevance of different projections relative to the chosen reference. The predictive synthesis distribution can be compared to the reference to assess how well the set of scenarios spans risks. This statistical comparison can focus on specific segments of the reference, to highlight which ‘regions’ of the risk outlook (eg, upside, downside, central) are more completely captured by a given scenario set.
The three April 2026 MPR scenarios collectively capture a broad range of inflation risks.
The April 2026 MPR scenarios captured the implications of different global energy-price paths and second-round effects for the UK economy. In Scenario A, the energy shock is relatively short-lived and demand weakness is assumed to prevent second-round effects in response to the shock. In Scenario B, energy prices peak at similar levels but remain higher over the forecast than in Scenario A, with second-round effects assumed to be modest. In Scenario C, energy prices rise sharply and remain elevated for a prolonged period, with much stronger second-round effects than in Scenario B.
Applying the synthesis approach to the inflation projections from Scenarios A, B and C reveals that all three are required to span risks to the inflation outlook.
To reach this conclusion, Bank staff have synthesised the scenarios against numerous reference distributions, capturing a range of views about the overall risk outlook. Here, we focus on one: inflation risks captured by the Decision Maker Panel (DMP) survey. That reference – shown in aqua in Chart 1 at the one-year horizon – is well-suited for this application because it provides probability distributions for CPI inflation based on responses from UK firms, who are pertinent in the transmission of second-round effects.
Chart 1: The synthesis of CPI inflation scenarios captures much of the distribution of risks perceived by firms
DMP-implied expectations for one year ahead UK CPI inflation versus scenario synthesis
Footnotes
- Notes: Chart plots probability density functions for one year ahead UK CPI inflation. The aqua distribution shows the expectations for UK CPI implied from the DMP survey in April 2026. This is constructed by fitting a skew-t distribution, developed by Azzalini and Capitanio (2003), through the 10th, 25th, 50th, 75th and 90th percentiles of the raw DMP data. The orange distributions show the synthesised predictive densities constructed from scenarios in the April 2026 MPR, conditioned on the market-implied path for interest rates in the 15 days to 22 April 2026.
- Source: Bank calculations.
The scenario weights suggest that the risks to inflation embedded in Scenario B appear most plausible through the lens of the DMP-implied reference. The synthesis places nearly two thirds of the weight on Scenario B, one third on Scenario C, and near zero on Scenario A. These weights are predicated on the statistical alignment between scenarios and the given reference distribution. Of course, policymakers may differ in their views on the overall risk outlook, captured by the reference distribution. They may also place different weights on scenarios, informed by narrative factors outside of the synthesis approach.
The resulting synthesised distributions, depicted in orange in Chart 1, show how the set of scenarios span inflation risks embedded in the DMP-implied reference. To highlight the contribution of Scenario C in spanning risks to inflation, we compare the synthesis of all three scenarios (solid) to a synthesis built from Scenarios A and B only (dashed). Visually, it is striking how the addition of Scenario C generates much greater probability mass in the synthesis density towards the right-side of the reference.
Quantitatively, the combination of Scenarios A, B and C spans 99% of risks to inflation in the central region (25th–75th percentiles) of the DMP-implied reference, as well as the right (50th–90th percentiles) and left-sides (10th–50th percentiles). That is, if you observed a random inflation outcome drawn from a segment of the reference, it would look statistically consistent with the outcomes implied by the scenario mixture 99 times out of 100.
In contrast, when Scenario C is omitted, the synthesis spans only 87%–89% of risks in the three regions of the reference – highlighting how all three scenarios are valuable for capturing risks to the inflation outlook.
Model-based policy projections capture different segments of market-implied expectations.
To explore policy-relevant risks, we extend the synthesis approach to analyse the illustrative model-based policy projections shown in the April 2026 MPR. These projections, described in Alati et al 2025, generate Bank Rate paths that minimise policymaker ‘losses’ through the lens of a macroeconomic model. As explained in the MPR, these exercises suggest policy paths that differ from the market curve, but they do not necessarily reflect policymakers’ assessment of the appropriate path of policy.
We compare the model-based policy projections to a market-implied reference distribution for Bank Rate – the one year ahead option-implied (risk-neutral) distribution, plotted in aqua in Chart 2.footnote [2] This reference is not without caveats – not least because risk premia mean the option-implied density need not reflect expectations alone. But, to the extent it is quoted with reference to expected Bank Rate, it offers a useful benchmark for the risks priced by market participants.
Chart 2: Syntheses of Bank Rate scenarios from model-based policy projections capture different portions of the market-implied reference distribution
Financial market option-implied expectations for one year ahead UK interest rates versus scenario synthesis
Footnotes
- Notes: Chart plots probability density functions for one year ahead UK Bank Rate. The aqua distribution shows the option-implied density for 12-month SONIA rate three months ahead on 22 April 2026, which represents the end of the April 2026 MPR 15-day conditioning window. The orange distributions show the synthesised predictive densities constructed from illustrative model-based policy projections on scenarios in the April 2026 MPR.
- Source: Bank calculations.
The model-based policy projections associated with Scenarios A and B are similar and imply a lower path for Bank Rate than in Scenario C. Reflecting this, the synthesis distribution for Bank Rate from Scenarios A and B only (dashed orange in Chart 2) aligns most with the left and central segments of the reference. It spans 84% of the 10th–50th percentiles and 74% of the 25th–75th, but just 41% of the right side (50th–90th percentiles).
The model-based policy projections around Scenario C appear distinct. The synthesis of all three scenarios (solid orange) is visually bimodal. Scenarios A and B collectively receive a weight of three fifths. Consequently, the first mode with the highest probability mass is associated with Scenarios A and B, and aligns closely with the synthesis of Scenarios A and B only. But the second mode – sitting to the right-side of the reference – is linked with Scenario C, which receives a two-fifths weight. This increases the share of risks spanned in the right segment of the reference substantially, to 94% (50th–90th percentiles), and contributes to the same spanning share for central risks (25th–75th percentiles).
Although the scenario weights reflect the statistical alignment between model-based policy projections and the market-implied reference, they do not account for the differential nature of risks to policy. So, they do not speak to the appropriate stance of monetary policy. Some risks, especially those linked to second-round effects, may require pre-emptive action to ‘lean against’. In contrast, aspects of other scenarios may reflect shocks that may only require policy action when materialising. Distinguishing these cases is a matter of policymaker judgement, outside of the scope of the synthesis.
Looking ahead: opportunities for further development.
As the results from this analysis show, the scenario synthesis approach can bridge the gap between scenario analysis and risk forecasting. It highlights – without offering insights on the appropriate policy response – how Scenarios A, B and C capture a broad range of differential risks to inflation and Bank Rate, which are embedded in firms’ and market-implied expectations, respectively.
We expect the synthesis approach to be particularly valuable when calibrating and choosing between different scenarios, as well as when monitoring how scenarios map into assessed risks as new data arrive.
The synthesis will, of course, only ever be one input to such deliberations, since its statistical grounding leaves it less well suited to exploring judgemental or narrative aspects of scenario design.
To strengthen the insights from this tool further, Bank staff are prioritising two development areas. First, as described at the inaugural Macro Modelling for Monetary Policy Forum, staff are developing new statistical tools to improve the construction of the reference distributions. This matters because different approaches to risk forecasting may vary in usefulness across the economic cycle. Second, motivated by the differing results for inflation and Bank Rate shown here, staff are expanding the approach to consider risks to inflation, growth and Bank Rate jointly, which would provide a more coherent assessment across key variables.
Bank Insights articles do not necessarily represent the views of the Bank of England’s policy committee members.
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The original work of Adrian et al (2025) distinguishes between the central projection and scenarios, as distinct inputs. However, given that the April 2026 MPR did not contain a central projection, Bank staff have adapted the methodology. In practice, this has been done by removing the constraint that the central projection has a weakly higher weight in the predictive synthesis distribution than the scenarios.
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Clews et al (2000) describes the construction of market-implied distributions around Bank Rate using options-market data.