Probability Levels at Various Future Intervals
In a groundbreaking development, analysts have devised a methodology to measure the likelihood of future short-term interest rates being constrained by the zero lower bound (ZLB) at different forecast horizons. This innovative approach, which relies on market prices to infer market expectations and mathematically adjust for the ZLB constraint, has been applied to both LIBOR and SOFR rates.
The methodology involves modeling the future short-term interest rates using a normal distribution, capturing both the expected level and uncertainty at each forecast horizon. The parameters of this distribution — mean and standard deviation — are extracted from market prices of derivatives such as futures, swaps, and interest rate caps that reflect market expectations and uncertainties about future interest rates.
Since nominal interest rates cannot realistically go below zero, the negative part of the normal distribution is truncated at zero, with any probability mass that would correspond to negative interest rates instead concentrated at zero, reflecting the ZLB. The ZLB probability is then the cumulative probability that the underlying normal variable falls below zero, i.e., the area under the distribution curve on the negative side before truncation.
For LIBOR, this methodology was applied until the end of 2021, while for SOFR, it has been in use since 2022. Given that SOFR tends to move closely with the federal funds rate, the implied distributions and ZLB probabilities derived from SOFR-based derivatives may reflect more directly the monetary policy rates and tend to be better aligned with the Federal Reserve's policy targets and expectations.
On May 27, 2025, the seven-year-ahead ZLB probability based on SOFR-related instruments was estimated at about 9%. This means there was about a 9% market-implied risk that the short-term interest rate at that horizon would be at the zero bound.
The Zero Lower Bound probabilities at Different Time Horizons are available for download as an Excel document (319 kb). This data provides measures at different time horizons in the future, such as three years ahead, and additional time horizons are also available in the downloadable Excel file.
This new measure offers valuable insights into the risk of the ZLB binding sometime in the future, allowing analysts to study the time variation in this risk robustly from derivatives tied to either LIBOR or SOFR. For related data on other interest rate probabilities, see Interest Rate Probability Distributions.
References:
1. The Federal Reserve Bank of San Francisco explains the methodology involving normal distributions for interest rates, truncation for ZLB, and differences in data sources for LIBOR vs. SOFR derivatives. 2. The paper "The Zero Lower Bound Remains a Medium-Term Risk" was published in 2025 by Cho, Sophia, Thomas M. Mertens, and John C. Williams. (FRBSF Economic Letter 2025-16, July 7) 3. The paper "What to Expect from the Lower Bound on Interest Rates: Evidence from Derivatives Prices" was published in 2021 by Thomas M. Mertens and John C. Williams. (American Economic Review 111(8, August)) 4. Figure 2 displays the time series of the ZLB probabilities at the 2-year, 5-year, 7-year, and 10-year horizons. 5. Figure 1 displays the term structure of ZLB probabilities up to 10 years ahead. 6. The distributions can be interpreted as market-based beliefs about constraints on future monetary policy. 7. The supplemental files for replication details can be found in the paper "What to Expect from the Lower Bound on Interest Rates: Evidence from Derivatives Prices."
In the context of the innovation in measuring Zero Lower Bound (ZLB) probabilities, this approach can be beneficial for investment decisions as it provides insights into the risk of future short-term interest rates being constrained by the ZLB at different forecast horizons. For instance, the seven-year-ahead ZLB probability based on SOFR-related instruments was estimated at about 9%, indicating a market-implied risk that short-term interest rates may reach the zero bound in the future. Thus, understanding and considering these ZLB probabilities in finance and investing could potentially influence long-term financial plans and strategies.
