Board of Governors of the Federal Reserve System

October 24, 2024

Drivers of Option-Implied Interest Rate Volatility

Cisil Sarisoy¹

Option-implied volatilities of U.S. short-term interest rates have risen sharply since late 2021, reaching their highest levels in over a decade. Although these measures declined moderately since early 2023, they remain at around the 70th percentile of their historical distribution.² This note links the implied volatility of short-term interest rates to macroeconomic uncertainty and highlights two fundamental drivers of short-term interest rate volatility over the past 30 years: inflation uncertainty and growth uncertainty. In a regression framework, I find that both have positive relationships with implied volatility during periods when the effective lower bound is not binding. That said, the relationships diverge over periods when rates are at, or near, the effective lower bound. The positive relationship between the inflation uncertainty and the implied volatility becomes stronger. In contrast, the relationship between the growth uncertainty and the implied volatility weakens and turns negative. The latter likely reflects the downward pressure on implied volatility from the return to the effective lower bound paired with the expectation of low rates for a protracted period, on the backdrop of the COVID-19 crisis.

Option-implied volatilities of interest rates in part reflect market participants' expectations about the volatility of an underlying interest rate at a specified horizon, and thus provide a signal about the market participants' uncertainty regarding future interest rates.³ The implied volatility of short-term interest rates is likely closely related to the uncertainty about the path of fed funds rate, and uncertainty about the fed funds rate should, in turn, reflect uncertainty about the outlook for inflation and real economic activity. To illustrate this, I construct survey-based disagreement measures for inflation and real GDP growth using the forecasts via Blue Chip Economic Indicators to proxy for inflation uncertainty and the real GDP growth uncertainty.⁴ Figure 1 shows the time series of the one-year-ahead option-implied volatility measure of one-year rate (dashed black lines) alongside measures of uncertainty of CPI inflation over the next year (red line in the left panel) and uncertainty of real GDP growth over the next year (blue line in the right panel).⁵ The shaded areas represent the effective lower bound (ELB) periods. Up until the onset of the pandemic, both inflation uncertainty and real GDP growth uncertainty have generally been positively correlated with the implied volatility.⁶ However, the implied volatility moved in opposite directions with the real GDP uncertainty in early 2020; the implied volatility declined notably while the real GDP uncertainty spiked.⁷ The decline in the implied volatility in this period is likely to be partly driven by the mechanical pull down from return to the effective lower bound in the U.S. and the expectation that rates would be pinned at low levels for a protracted period amid the COVID-19 crisis.⁸

Figure 1. Interest Rate Volatility and Survey-Based Uncertainty (Disagreement) Measures of CPI and Real GDP Growth

Next, I run regressions to show the effects of inflation uncertainty and real GDP uncertainty on option-implied interest rate volatility empirically. I estimate two regression specifications with the option-implied interest rate volatility as the dependent variable. In the first specification, I include the uncertainty measures for inflation over the next year and real GDP growth over the next year as the explanatory variables. I subsequently expand the specification to account for additional variables of interest—a dummy variable indicating the ELB periods and interactions of the ELB dummy variable with the inflation uncertainty and the real GDP growth uncertainty measures. These interaction terms enable me to capture whether the relationship between the implied volatility and the uncertainty measures differ between the ELB periods and the periods when the ELB is not binding. All independent variables are standardized by subtracting their unconditional mean and dividing by their unconditional standard deviations, to make the regression coefficients easy to compare and interpret. Both specifications are estimated using monthly data from January 1995 to July 2024.⁹

Table 1 summarizes the regression results. As shown in column 1, there is a positive and statistically significant relationship between inflation uncertainty and implied volatility, indicating that a higher inflation uncertainty is associated with a higher implied volatility.¹⁰ The real GDP growth uncertainty, however, does not have a statistically significant relationship with the implied volatility.¹¹ This specification explains 16 percent of the variation in implied volatility. The regression results in column 2 show that adding interaction effects between the ELB dummy and the measures for inflation uncertainty and the real GDP growth uncertainty adds substantial explanatory power. The relationship of the implied volatility with the uncertainty measures exhibits variation between the periods when ELB is binding and not binding. When the ELB is not binding, inflation uncertainty and the real GDP uncertainty both have positive, economically and statistically significant relationships with the implied volatility. As shown, a one standard deviation increase in inflation uncertainty is associated with a 10-basis-point increase in implied volatility for inflation uncertainty, and a one standard deviation increase in real GDP growth uncertainty is associated with a 22-basis-point increase in implied volatility during the periods when the ELB is not binding. However, the regression results show that, when the ELB is binding, the relationship between the inflation uncertainty and the implied volatility becomes stronger, and the relationship between real GDP uncertainty and the implied volatility weakens and turns negative (Table 1, column 2).¹² The latter likely reflects the downward pressure on implied volatility from the return to the effective lower bound paired with the expectation of low rates for a protracted period amid COVID-19 crisis. This specification explains almost 60 percent of the variation in implied short-term interest rate volatility.

Table 1: Explaining Option-Implied Interest Rate Volatility

Finally, considering the results from the second specification, I take a closer look at the changes in the implied short-term interest rate volatility since its peak in March 2023.¹³ As shown in Table 2, implied short-term interest rate volatility declined moderately since March 2023, by about 45 basis points. The model-based prediction entirely accounts for the decline in implied volatility, and more than half of the predicted decline is due to the decline in inflation uncertainty.

Table 2: Recent Movements in Option-Implied Interest Rate Volatility

References

Altig, D., Baker, S., Barrero, J.M., Bloom, N., Bunn, P., Chen, S., Davis, S.J., Leather, J., Meyer, B., Mihaylov, E., Mizen, P., Parker, N., Renault, T., Smietanka, P., Thwaites, G., 2020. Economic uncertainty before and during the COVID-19 pandemic. J. Public Econ. 191, 104274.

Cascaldi-Garcia, Danilo, Cisil Sarisoy, Juan M. Londono, Bo Sun, Deepa D. Datta, Thiago Ferreira, Olesya Grishchenko, Mohammad R. Jahan-Parvar, Francesca Loria, Sai Ma, Marius Rodriguez, Ilknur Zer, and John Rogers. 2023. "What Is Certain about Uncertainty?" Journal of Economic Literature, 61 (2): 624–54.

Dräger, Lena and Lamla, Michael J., Disagreement à la Taylor: Evidence from Survey Microdata (April 24, 2015). KOF Working Paper No. 380.

Jurado, Kyle, Sydney C. Ludvigson, and Serena Ng (2015). "Measuring Uncertainty," American Economic Review 105 (3): 1177–1216.

Sarisoy, Cisil (2023). "Elevated Option-Implied Interest Rate Volatility and Downside Risks to Economic Activity," FEDS Notes. Washington: Board of Governors of the Federal Reserve System, December 22, 2023, https://doi.org/10.17016/2380-7172.3404.