How we derive interest rate probabilities and assess central bank policy stance
Technical framework for market-implied policy probability extraction and normative rate benchmarking
What this site does: It provides two analyses for each central bank covered:
How it works:
A key challenge: Fed Funds futures directly track the Fed's policy rate, the Federal Funds Rate. No such direct link exists for the ECB or BoE. The closest proxies are ESTR for the ECB and SONIA for the BoE, both of which trade 5–15 basis points below the respective policy rates. This site assumes the current spread remains constant over the forecast horizon.
Validation: Over 90% directional accuracy across 95 central bank decisions (2020–2024).
Interactive tool: A free Excel calculator is available for download, allowing users to replicate the probability methodology and experiment with different futures prices.
Dual methodology framework:
Key contribution: Extension of the CME FedWatch methodology to ESTR and SONIA under a constant-spread assumption for 6–12 month horizons. Out-of-sample performance: 96.3% directional accuracy, 4.1pp MAE, Brier score 0.041.
Tools: A full Excel implementation is available (download below) with transparent formulas and no macros.
Central bank policy analyzed through two complementary lenses
Question: What will central banks do next?
Method: Futures market analysis
Output: Probabilities for rate changes at each upcoming meeting
Example: "75% chance of a 25bp cut in March"
Sections: 1–3 below
Question: Should rates be higher or lower?
Method: Economic models (Taylor Rule, Okun's Law)
Output: Dovish / Neutral / Hawkish classification
Example: "Rates 50bp above Taylor Rule → Hawkish stance"
Sections: 4–5 below
These methodologies complement each other. Probability forecasts reflect what markets expect; the policy stance assessment reflects what economic fundamentals suggest. Each central bank page presents both.
The industry standard for extracting policy expectations from futures markets
Interest rate futures aggregate the expectations of thousands of professional investors who commit real capital to positions on where rates are headed. The CME FedWatch methodology converts those prices into probabilities in three steps.
Step 1: Futures contracts reflect average rates. A Fed Funds futures contract settles based on the average effective federal funds rate for a given month. If the current rate is 5.00% and the June contract implies 4.75%, the market expects the average rate in June to be 4.75%.
Step 2: Account for meeting timing. If the Fed meets on June 15, the rate for the first 15 days of the month is the pre-meeting rate (5.00%). For the remaining 15 days, it is whatever the Fed decides. The futures price captures the weighted average of both periods.
Step 3: Solve for the implied post-meeting rate. Using calendar math, we solve for the post-meeting rate that is consistent with the observed futures price. If that rate is 4.875% — halfway between 5.00% and 4.75% — the implication is a roughly 50% chance of no change and a 50% chance of a 25bp cut.
Current rate: 4.375%
June futures price: 95.6738 (implies a rate of 4.3262%)
Fed meeting: June 18 (day 18 of 30)
Calculation: Before the meeting (days 1–17), the rate is 4.375%. After the meeting (days 18–30), it is unknown. Working backward from the futures price yields a post-meeting rate of 4.262%.
Result: The implied change is −11.3bp, which falls between 0 and −25bp. This translates to a 54.8% probability of no change and a 45.2% probability of a 25bp cut.
For meetings further out, the model uses an "expanding tree." Each meeting branches into possible outcomes — rate up, down, or unchanged — and the model assigns probabilities to each branch based on futures prices. Tracking all paths through the tree yields the probability of any given rate level at any future meeting.
For further details, see the dedicated page on the Expanding Tree Method.
Let \(F_m\) be the futures rate for month \(m\), \(R_{pre}\) the rate before the meeting, \(R_{post}\) the rate after, \(d_{pre}\) days before the meeting, and \(d_{post}\) days after:
Solving for \(R_{post}\):
The implied rate change \(\Delta R = R_{post} - R_{pre}\) is mapped to probabilities via linear interpolation between adjacent 25bp outcomes. If \(\Delta R\) falls between outcomes \(O_i\) and \(O_{i+1}\):
The expanding tree extends single-meeting extraction recursively. Given futures prices \(F_1, F_2, \ldots, F_n\) for \(n\) meetings, transition probabilities \(p_{ij}^t\) at each node satisfy normalization (\(\sum_j p_{ij}^t = 1\)), a martingale constraint (expected rate equals the futures-implied rate), and path consistency (probabilities aggregate correctly across branches).
Computational complexity is \(O(n^2 \cdot m)\), where \(n\) = possible rate levels and \(m\) = number of meetings.
The constant-increment assumption breaks down in crisis periods. Risk premia embedded in futures can bias probability estimates. The methodology is most reliable for Fed Funds, where futures directly track the policy instrument, as opposed to ESTR or SONIA, which are market-determined rates with variable spreads to policy rates.
Let \(P_t(r_i)\) be the probability of rate \(r_i\) at meeting \(t\). Transition probabilities \(p_{ij}^t\) from \(r_i\) to \(r_j\) satisfy:
The system is solved recursively, extracting \(p_{ij}^t\) from futures prices and prior probabilities. Computational complexity is \(O(n^2 \cdot m)\), where \(n\) = possible rates and \(m\) = meetings.
CME FedWatch Tool and data are proprietary to CME Group. Visit CME's official tool for authoritative Federal Reserve probabilities. This work focuses on extending the methodology to other central banks.
Why extending the methodology to European central banks requires modification
The CME methodology works cleanly for the Federal Reserve because Fed Funds futures directly track the Fed's policy rate. For the ECB and Bank of England, no such direct link exists.
| Central Bank | Policy Rate | Futures Contract | What Futures Track | The Gap |
|---|---|---|---|---|
| Federal Reserve | Fed Funds Rate | Fed Funds Futures | Fed Funds Rate | None (1:1 match) |
| European Central Bank | Deposit Facility Rate (DFR) | ESTR Futures | ESTR (market rate) | ~8–15bp below DFR |
| Bank of England | Bank Rate | SONIA Futures | SONIA (market rate) | ~3–7bp below Bank Rate |
ESTR (Euro Short-Term Rate) and SONIA (Sterling Overnight Index Average) are based on actual overnight lending transactions. They consistently trade below official policy rates for three reasons. First, non-bank participants such as money market funds, pension funds, and insurers cannot deposit directly with central banks and therefore accept slightly lower rates from commercial banks. Second, when excess liquidity is abundant — as during quantitative easing — spreads widen; when liquidity tightens, they narrow. Third, bank leverage ratios, liquidity coverage requirements, and balance sheet constraints all affect intermediation and, by extension, the spread.
For short-term forecasts covering the next two to four meetings (typically 6–12 months), this site assumes the current spread remains constant. This is reasonable because spreads change slowly absent major policy announcements, the forecast horizon is shorter than typical balance sheet adjustment periods, and the assumption keeps calculations transparent and replicable.
Important caveat: If the ECB or BoE announces a significant change in balance sheet policy — such as accelerated quantitative tightening — the spread assumption may require adjustment.
A 5bp error in spread assumptions can shift probability estimates by 10–20 percentage points. Accurate spread calibration is critical.
Under floor systems with abundant reserves, ESTR and SONIA reflect general collateral rates for non-bank financial institutions — money market funds, pension funds, insurers — that lack direct central bank deposit access. Segmented market access and differing regulatory constraints create a persistent wedge below the policy rate.
Primary spread determinants:
For forecast horizons of 6–12 months with no announced regime shifts, this site uses the current observed spread. The justification rests on mean-reverting behavior within regimes, a forecast horizon shorter than typical balance sheet adjustment periods (18–24 months for QT programs), parsimony, and transparency.
Implementation: (1) Observe the current spread \(s_t = DFR_t - ESTR_t\). (2) Adjust futures-implied rates by \(s_t\). (3) Apply the standard expanding-tree methodology to adjusted rates. (4) Normalize probabilities.
The constant-spread assumption is unreliable during announced QE/QT transitions, significant reserve drainage or injection programs, and regulatory changes affecting money market structure. In such cases, spread forecasts should incorporate announced policy paths and historical spread behavior during analogous episodes. Regime-switching models improve accuracy but add considerable complexity.
ECB DFR-ESTR spread:
BoE Bank Rate-SONIA spread:
What interest rates "should" be, given economic fundamentals
Market probabilities show what traders expect central banks to do. Theoretical rates show what economic conditions suggest they should do. The gap between the two is informative.
The most widely used model is the Taylor Rule, which calculates a recommended interest rate based on two inputs: how far inflation is from the central bank's target (usually 2%), and how far the economy is from full capacity — a concept economists call the "output gap."
Theoretical Rate = Neutral Rate + 1.5 × (Inflation − Target) + 0.5 × Output Gap
Example:
Taylor Rule rate = 2.5 + 1.5 × (3.5 − 2) + 0.5 × 1 = 5.25%
If the actual policy rate is 4.75%, it sits 50bp below where the Taylor Rule says it should be — a modestly accommodative stance.
The output gap measures whether the economy is running above or below its potential. One standard method for estimating it is Okun's Law, which links unemployment to economic output. When unemployment falls below its natural rate, the economy is likely running hot (positive output gap). When unemployment exceeds the natural rate, there is slack (negative output gap).
Each central bank has distinct characteristics, and the models are calibrated accordingly:
Full technical details are on the respective model pages.
The generalized Taylor Rule specification:
Where:
Three methods are employed:
Detailed specifications are on each central bank's model page:
Individual model pages document estimation methodology, parameter calibration, and backtesting results.
Comparing actual rates to theoretical rates
Each central bank page includes a chart of the historical rate gap — the difference between the actual policy rate and the Taylor Rule's recommended rate.
Rate Gap = Actual Rate − Theoretical Rate
Interpretation:
Consider the ECB in mid-2023:
Interpretation: Despite a rapid hiking cycle through 2022–2023, ECB policy remained slightly accommodative relative to the Taylor Rule, suggesting scope for further tightening had inflation persisted.
The rate gap offers a framework for assessing policy bias (whether the next move is more likely a hike or a cut), the reasonableness of market pricing, and whether policy may be too tight (risking recession) or too loose (risking persistent inflation). Combined with probability forecasts, it provides a more complete picture: what markets expect versus what fundamentals suggest.
Policy stance is classified via threshold-based rules:
Where \(i_t\) is the actual policy rate and \(\hat{i}_t\) is the Taylor Rule prescription. The ±25bp threshold reflects measurement uncertainty in the output gap and neutral rate estimates.
Rate gap charts provide useful historical perspective:
Taylor Rule-based assessment has well-documented limitations:
Rate gaps are presented as one input to policy assessment, not as definitive judgments. Central banks weigh a broader set of indicators than any single rule captures.
Planned expansions and methodology enhancements
Several enhancements are in the research phase:
The current methodology prioritizes simplicity and transparency over marginal accuracy gains from more complex models.
This is an evolving project. Questions, corrections, and methodological suggestions are welcome — please get in touch.
An Excel tool for exploring the expanding-tree methodology
This Excel workbook implements the probability calculation methodology described above. Users can modify futures price inputs and observe how rate probabilities evolve across multiple policy meetings.
Excel workbook with binary tree calculations, visual probability tree, and automatic updates. No macros — pure formula-based calculations.
Key feature: The calculator distinguishes between meeting months (when rates can change) and non-meeting months (when rates remain constant). This distinction is critical for accurate probability calculation.
Academic sources and data sources
CME FedWatch Tool and data are proprietary to CME Group. Visit CME's official tool for authoritative Federal Reserve probabilities. My work focuses on extending their methodology to other central banks.