Interest Rate Probability Distributions

Interest Rate Probability Distributions Implied by Derivatives Prices is a daily measure of the distribution of future short-term interest rates, calculated from prices of fixed-income derivatives using the methodology of Mertens and Williams (2021).

Different percentiles of the distribution characterize the likelihood with which future short-term interest rates fall into a certain range. Mertens and Williams (2021) uses caps and floors based on LIBOR. The updated series on this page switch from market prices based on LIBOR to caps and floors based on SOFR rates at the beginning of 2022. The plots display the distribution of interest rates at the 3-year and 7-year horizons on this page and available at additional frequencies in the downloadable Excel file. A rectified Gaussian distribution underlies each estimate, taking the zero lower bound on interest rates into account. For additional details, see Mertens and Williams (2021) and the paper’s online appendix.

The daily measures can be used to study time-variation in projections for interest rates. In particular, the distributions capture the average level of forward rates, the uncertainty surrounding them, as well as asymmetries in the distribution. The estimation takes the possibility of a binding lower bound on interest rates into account. Since short-term interest rates tend to comove tightly with the federal funds rate, the distributions can be interpreted as market-based beliefs about future monetary policy.

Figure 1: Interest Rate Probability Distributions, Three Years Ahead

Notes: Data reflect 20-day moving averages of 3-year-ahead interest rate projections based on caps data. Lines show the average and median, along with selected forecast densities of 85% and 15%. Additional forecast densities and projection horizons available in downloadable data file below.

Figure 1: Interest Rate Probability Distributions, Three Years Ahead

Figure 2: Interest Rate Probability Distributions, Seven Years Ahead

Notes: Data reflect 20-day moving averages of 7-year-ahead interest rate projections based on caps data. Lines show the average and median, along with selected forecast densities of 85% and 15%. Additional forecast densities and projection horizons available in downloadable data file below.

Figure 2: Interest Rate Probability Distributions, Seven Years Ahead

Reference

Mertens, Thomas M., and John C. Williams. 2021. “What to Expect from the Lower Bound on Interest Rates: Evidence from Derivatives Prices.” American Economic Review 111(8, August).

Download Data

Daily Interest Rate Probability Distributions (Excel file, 203 kb)