Fed Put in the Equity Options Markets: Dahiya, Kamrad, Poti & Siddique (2026)

What this is. The paper’s core results, the monetary policy identification design (Taylor Rule deviation combined with the Wu-Xia shadow rate), and the regression specifications with enough detail to know what it found and how, without reading all 14 pages. To replicate or extend it, read the full source at the original.

TL;DR

The paper tests whether the “Fed Put” (Greenspan Put) is detectable in equity options prices. The premise: if investors believe the Federal Reserve will support markets during downturns, exchange-traded put options are partially substituted by the Fed’s implicit backstop, so out-of-the-money put implied volatility should be lower during accommodative monetary policy periods. Using 1,342 weekly observations of S&P 500 (SPX) and S&P 100 (OEX) index option implied volatilities from OptionMetrics (January 1996 to December 2021), the paper reports that put implied volatility is 3 to 5 percentage points lower during accommodative periods, a 10% to 15% reduction relative to the unconditional mean. This result comes from the binary support measure; the effect is amplified in high-risk-aversion regimes per Bekaert, Engstrom, and Xu (2021). The paper also reports stronger negative continuous-measure coefficients before 2008 and mostly insignificant adjusted post-crisis coefficients, but its stated continuous coding (shadow rate minus Taylor-rule rate) means more accommodation is a more negative regressor, so the negative slope implies higher rather than lower volatility under accommodation. That conflicts with the paper’s interpretation. Univariate and binary IV-GMM estimates support lower volatility during Fed support; the authors cannot distinguish a mechanical zero-lower-bound effect from a lasting shift in expectations after the crisis.

Core results

Magnitudes and significance are as reported. Locators point into the source PDF.

#	Result	Locator	Magnitude
R1	Accommodative Fed stance (FedSupport) lowers S&P 500 put implied volatility across all 11 moneyness levels (univariate)	Table 1, Panel A, p. 8	β₁ = -3.32 (t=-20.48) at moneyness=50; -5.33 (t=-37.48) at moneyness=100; all 11 categories 1% significant
R2	Effect is concentrated in high-risk-aversion regimes; negligible when risk aversion is low	Table 2, Panel A, p. 9	Quintile 5 (highest RA): β₁ = -6.27 (t=-14.44); Quintile 1 (lowest RA): β₁ = 0.09 (t=0.50, not significant); at moneyness=50
R3	Pre-crisis (1996-2007) multivariate OLS effect is nearly 3x the full-sample estimate	Table 5, p. 11	Pre-crisis OLS: β₁ = -0.659 (t=-6.746); full-sample OLS: β₁ = -0.223 (t=-2.668)
R4	Post-crisis (2009-2021) continuous-measure coefficients are insignificant in the multivariate regression	Table 5, p. 11	Post-crisis OLS: β₁ = -0.102 (t=-0.759, not significant); post-crisis IV-GMM: not significant
R5	Pre-crisis IV-GMM estimate is approximately 2x the OLS estimate	Table 5, p. 11	Pre-crisis IV-GMM: β₁ = -1.205 (t=-8.152), 1% significant
R6	Binary FedSupport measure corroborates OLS; pre-crisis IV-GMM also strongly negative	Table 6, p. 13	Full-sample OLS: β₁ = -1.827 (t=-6.172); pre-crisis OLS: β₁ = -2.674 (t=-9.122); pre-crisis IV-GMM: β₁ = -3.969 (t=-8.571)
R7	Alternative monetary policy proxies (money-market-futures changes) confirm the negative relation	Table 7, p. 13	ΔMP1 OLS: β₁ = -9.427 (t=-51.566); ΔMP1 IV-GMM: β₁ = -80.292 (t=-1.813, 10% significant)
R8	The FedSupport coefficient shifts from positive to negative as risk aversion rises	Table 2, Panel A, p. 9	At moneyness 50: Q2 β₁ = 2.20 (t=13.86, 1%); Q3 = -0.54 (t=-3.02, 5%); Q4 = -3.49 (t=-17.78, 1%); Q5 = -6.27 (t=-14.44, 1%)
R9	Univariate results retain a negative Fed Put estimate in both crisis subperiods	Table 3, Panel A and B, p. 10	At moneyness 50: pre-crisis β₁ = -2.442 (t=-14.11); post-crisis = -1.737 (t=-6.04); at 10-day maturity: pre = -2.246 (t=-10.12); post = -6.105 (t=-19.38); all 1% significant
R10	S&P 100 results are mixed across subperiods	Table 4, Panel A, p. 10	At moneyness 50: full-sample β₁ = -1.49 (t=-9.37); pre-crisis = 1.04 (t=6.80); post-crisis = -6.35 (t=-25.90); full and post estimates 1% significant
R11	Alternative regime classifications mostly reproduce the S&P 500 result	§4.1, pp. 7-8 (Online Appendix results summarized in text)	MSDR β₁ ranges from -3.34 to -4.26 across moneyness and maturity buckets, all 1% significant; HMM estimates are negative and significant except at moneyness 50 and 55
R12	Binary FedSupport IV-GMM reverses sign in the post-crisis period	Table 6, p. 13	Post-crisis β₁ = 7.841 (t=4.023, 1% significant); pre-crisis β₁ = -3.969 (t=-8.571, 1% significant)

Overall (paper’s conclusion). The binary FedSupport results show lower implied volatility during accommodative periods, consistent with investors treating the Fed’s implicit backstop as a partial substitute for put protection. The pattern is amplified in high-risk-aversion regimes, aligning with the meta moral hazard mechanism of Miller, Weller, and Zhang (2002). The continuous specification’s reported negative coefficients are stronger before 2008 and mostly insignificant after the crisis, but their direction conflicts with the paper’s stated shadow-minus-Taylor coding: under that coding, more accommodation means a lower regressor value, and a negative slope predicts higher implied volatility. The binary indicators, by contrast, have a direct interpretation and support the Fed Put. The authors say they cannot determine whether the post-crisis pattern reflects the zero lower bound’s mechanical effect on option prices or a persistent shift in expectations.

Theory / model

The paper has no formal model of its own. It tests the theoretical framework of Miller, Weller, and Zhang (2002), who distinguish two cases for the Fed Put’s effect on option prices. In the first (complete-credibility) case, investors fully believe the Fed will prevent large market declines; return distributions exhibit a truncated downside and a fatter upside, and variation in policy would have no impact on beliefs or option prices. In the second (partial-credibility) case, monetary policy stance shifts investor beliefs about the probability and magnitude of Fed intervention, generating a negative cross-price effect between accommodative policy and put implied volatility. The paper tests the partial-credibility case empirically. While Miller, Weller, and Zhang (2002) and Drechsler, Savov, and Schnabl (2018) discuss theoretical mechanisms through which central bank intervention distorts asset prices, prior empirical evidence had been scarce.

Identification via the Taylor Rule (§2.1, p. 3): Monetary policy stance is identified through deviations of the effective fed funds rate from the Taylor (1993) benchmark rate. The original Taylor Rule specification is (Eq. 1, p. 3):

$$i = r^* + \pi + w_1(\pi - \pi^*) + w_2(y - y^*) \tag{1}$$

where $i$ is the nominal federal funds rate, $r^* = 2\%$ is the target real FFR, $\pi$ is the inflation rate, $\pi^* = 2\%$ is the target inflation rate, $y$ is log real output, $y^*$ is log potential output, and $w_1 = w_2 = 0.5$ in the original specification. The paper also tests variants labeled Final Taylor Rule 1_1, 1_2, 2_1, 2_2, and 2_3 that modify the inflation measure and output-gap weight.

For ZLB periods when the observed FFR cannot capture the full accommodation of unconventional policy, the paper substitutes the Wu and Xia (2016) shadow fed funds rate. This rate is derived from a factor-augmented VAR (FAVAR) model with three latent factors; the Atlanta Fed maintains updated estimates. When the shadow rate is above 0.25%, it equals the model-implied one-month interest rate by construction; it extends below zero at the ZLB.

FedSupport measure (§2.1, pp. 3-4): Two variants are constructed:

• Continuous: (Wu-Xia shadow rate) minus (Taylor Rule implied rate); more negative = more accommodative. This stated coding conflicts with the negative continuous-regression coefficients being interpreted as lower volatility during accommodation: the negative slope predicts higher volatility when the regressor becomes more negative.
• Binary: indicator equal to 1 when the shadow rate falls below the Taylor Rule benchmark (Fed supports markets), and 0 otherwise

For the binary support indicator, the key prediction is β₁ < 0: when the Fed provides implicit downside protection, investors demand less explicit insurance from put options. For the continuous shadow-minus-Taylor measure, the same substantive prediction implies β₁ > 0 because more accommodation makes the regressor more negative. The paper nevertheless interprets negative continuous-regression coefficients as evidence of the Fed Put. The results of Adrian et al. (2020), who show accommodative interest rate policy shifts rather than eliminates macroprudential risk over time, motivate the expectation of a structural break around the Global Financial Crisis.

Method

The paper applies OLS panel regression and IV-GMM to weekly options data. The baseline specification (Eq. 2, p. 4) is:

$$\sigma(\text{Put})_{i,t} = \beta_0 + \beta_1 \times \text{FedSupport}_t + \phi' \text{Controls}_{i,t} + u_t \tag{2}$$

where $\sigma(\text{Put})_{i,t}$ is the implied volatility of put option $i$ in week $t$, expressed as a percentage, and $\text{FedSupport}_t$ captures the monetary policy stance. It builds on panel-regression as the baseline estimator.

Endogeneity is addressed via instrumental-variables estimation combined with gmm. Both FedSupport and RiskAversion are potentially endogenous: unobserved macroeconomic or financial variables could influence both the Fed’s policy stance and investors’ risk preferences simultaneously. The IV-GMM estimator (Appendix A, Eq. 9, p. 13) is:

$$\hat{\beta}_{\text{GMM}} = (\mathbf{X}'\mathbf{Z}\mathbf{W}\mathbf{Z}'\mathbf{X})^{-1} \mathbf{X}'\mathbf{Z}\mathbf{W}\mathbf{Z}'\mathbf{y} \tag{9}$$

where $\mathbf{X}$ is the matrix of potentially endogenous regressors, $\mathbf{Z}$ is the instrument matrix, and the text defines $\mathbf{W}$ as a consistent estimate of the covariance matrix of moment conditions. The printed Eq. 9 uses $\mathbf{W}$ directly, while the accompanying text says the optimal second-step weighting matrix is the inverse of a HAC covariance estimate; the notation is internally inconsistent, so the equation above follows the printed formula (Appendix A, Eq. 9, p. 13). The paper jointly estimates the option-volatility equation and two first stages. In Appendix A, those first stages are restated as:

$$\text{FedSupport}_t = \kappa_0 + \kappa_1 \text{LaborMarket}_{t-1} + \kappa_2 \text{SP500}_{t-1} + \kappa_3 \text{FinStability}_{t-1} + \kappa_4 \text{SP500PE}_{t-1} + u_t \tag{11}$$ $$\text{RiskAversion}_t = \gamma_0 + \gamma_1 \text{LaborMarket}_{t-1} + \gamma_2 \text{SP500}_{t-1} + \gamma_3 \text{FinStability}_{t-1} + \gamma_4 \text{SP500PE}_{t-1} + \eta_t \tag{12}$$

Appendix A, Eqs. 11-12 (p. 14) use the lagged Kansas City Fed labor-market index, S&P 500 return, St. Louis Fed financial-stress index, and S&P 500 price-earnings ratio. These duplicate the instrument specifications in Eqs. 6-7. The instrumented equations have no fixed effects reported; robust/HAC inference is used, and the continuous-specification samples are 132,066 observations overall, 60,885 pre-crisis, and 66,033 post-crisis (Table 5, p. 11). The binary-specification samples are the same sizes (Table 6, p. 13). The paper calls the system exactly identified, but lists four excluded instruments for two endogenous regressors, which would ordinarily imply overidentification; it does not reconcile this count.

Empirical specifications

Data construction (§3, p. 5): Daily option implied volatility data come from the OptionMetrics Ivy DB, compiled from 3:59 PM EST closing prices for S&P 500 (CBOE ticker: SPX) and S&P 100 (CBOE ticker: OEX) index options. Black-Scholes implied volatility is computed for each option using the underlying index price, dividend yield, risk-free rate, time to maturity, and strike price. The volatility surface is reconstructed via cubic spline interpolation. Weekly observations are taken every Wednesday. Moneyness is defined as (strike price / current index price) × 100, so an out-of-the-money put has moneyness < 100.

Univariate (Eq. 3, p. 7; produces R1, R2):

$$\sigma(\text{Put})_{i,t} = \beta_0 + \beta_1 \times \text{FedSupport}_t + u_t \tag{3}$$

Estimated separately for each of 11 moneyness levels (50, 55, …, 100) and 9 maturity buckets (10 to 90 days). The binary FedSupport indicator is used. Panel A of Table 1 (p. 8) aggregates across maturities for each moneyness level; Panel B aggregates across moneyness for each maturity. Table 2 (p. 9) stratifies by quintile of the Bekaert, Engstrom, and Xu (2021) relative risk aversion index to test the heterogeneity prediction (R2).

Multivariate OLS (Eq. 4, p. 10; produces R3, R4):

$$\sigma(\text{Put})_{i,t} = \beta_0 + \beta_1 \times \text{FedSupport}_t + \beta_2 \times \text{Moneyness}_{i,t} + \beta_3 \times \text{Expiration}_{i,t} + \beta_4 \times \text{RiskAversion}_t + \varepsilon_{i,t} \tag{4}$$

The continuous measure of FedSupport (shadow rate minus Taylor Rule rate) is used in Table 5 (p. 11); the binary measure in Table 6 (p. 13). $\text{RiskAversion}_t$ is the Bekaert, Engstrom, and Xu (2021) relative risk aversion index, sampled at weekly frequency. Standard errors are robust using the HAC procedure of Chang and McAleer (2015). The sample splits at December 31, 2007 (pre-crisis: 1996-2007) and January 1, 2009 (post-crisis: 2009-2021).

IV-GMM structural (Eq. 5, p. 11; produces R5):

$$\sigma(\text{Put})_{i,t} = \beta_0 + \beta_1 \times \widehat{\text{FedSupport}}_t + \beta_2 \times \text{Moneyness}_{i,t} + \beta_3 \times \text{Expiration}_{i,t} + \beta_4 \times \widehat{\text{RiskAversion}}_t + \varepsilon_{i,t} \tag{5}$$

Both FedSupport and RiskAversion are instrumented. The first-stage equations (Eqs. 6-7, p. 12) use four lagged macro indicators as instruments:

$$\text{FedSupport}_t = \kappa_0 + \kappa_1 \text{LaborMkt}_{t-1} + \kappa_2 \text{SP500}_{t-1} + \kappa_3 \text{FinStab}_{t-1} + \kappa_4 \text{PE}_{t-1} + u_t \tag{6}$$ $$\text{RiskAversion}_t = \gamma_0 + \gamma_1 \text{LaborMkt}_{t-1} + \gamma_2 \text{SP500}_{t-1} + \gamma_3 \text{FinStab}_{t-1} + \gamma_4 \text{PE}_{t-1} + \eta_t \tag{7}$$

where LaborMkt is the Kansas City Fed Labor Market Conditions Index, SP500 is the lagged S&P 500 return, FinStab is the FRB St. Louis Financial Stress Index, and PE is the lagged S&P 500 Price-Earnings Ratio. The paper calls the system exactly identified, but lists four excluded instruments for two endogenous regressors, which would ordinarily imply overidentification; it does not reconcile this count. Instrument relevance is confirmed: Kleibergen-Paap LM test chi² = 76.557 (rejects under-identification, p < 0.01); weak instruments null rejected at chi² = 24.462 (p < 0.01) (footnote 15, p. 11).

Alternative MP proxies (Eq. 8, p. 12; produces R7):

$$\Delta\sigma(\text{Put})_{i,t} = \beta_0 + \beta_1 \times \Delta MP_t + \beta_2 \times \text{Moneyness}_{i,t} + \beta_3 \times \text{Maturity}_{i,t} + \beta_4 \times \text{RiskAversion}_t + \varepsilon_{i,t} \tag{8}$$

where $\Delta MP_t$ is the weekly change in a money-market futures price index: MP1 is the 8-quarter-ahead 3-month Eurodollar futures level (100 minus yield); MP2 is the 3-month 30-day Fed Funds futures level. An increase in MP1 or MP2 corresponds to expected monetary easing; a negative β₁ confirms the Fed Put. Table 7 (p. 13) reports OLS and IV-GMM estimates for both proxies.

Subperiod and cross-index univariate checks (Eq. 3, pp. 7-8; Tables 3-4, p. 10; produces R9-R10): Eq. 3 is estimated separately for each moneyness or maturity bucket on the 1,342 weekly-observation sample, with no controls or fixed effects. Table 3 splits SPX weeks into 1996-2007 and 2009-2021; Table 4 repeats the analysis for OEX over the full period and both subperiods. Reported parenthetical values are t-statistics, with significance from t-tests. Table 4’s pre-crisis OEX estimates are positive for moneyness 50-65, unlike its full-sample and post-crisis estimates.

Inference, sample, and endogeneity checks (Eqs. 4-8, pp. 10-12; Tables 5-7, pp. 11-13; produces R3-R7 and R12): Tables 5-6 estimate option-week regressions with moneyness, expiration, and weekly risk-aversion controls and no fixed effects reported. Robust standard errors are reported; the paper describes the treatment as HAC (Table 5 discussion, p. 11; tables report robust standard errors). Full-sample OLS uses 132,858 observations, while IV-GMM uses 132,066; the corresponding pre- and post-crisis counts are 61,182 and 66,429 for OLS, and 60,885 and 66,033 for IV-GMM. Tables 5-6 instrument FedSupport and risk aversion using the four lagged macro series in Eqs. 6-7. Table 7 estimates first-difference regressions in Eq. 8 for 130,743 (MP1 OLS), 129,960 (MP1 IV-GMM), 130,644 (MP2 OLS), and 129,861 (MP2 IV-GMM) option-week observations. Its table note reports robust standard errors; no fixed effects are specified. The reported estimates use t-statistics and *, **, *** for 10%, 5%, and 1% significance. Table 6’s post-crisis binary IV-GMM coefficient is positive and significant (R12), unlike the continuous measure in Table 5.

Robustness: Markov Switching Dynamic Regression (MSDR) and Hidden Markov Models (HMM) are used as alternative identification strategies for Fed support regimes; the main-text discussion summarizes their Online Appendix estimates (R11; §4.1, pp. 7-8). Results are also reported for S&P 100 (OEX) index options (Table 4, p. 10; R10).

Datasets used

Dataset	Role in paper	Wiki page
OptionMetrics Ivy DB (S&P 500 SPX, S&P 100 OEX)	Primary data: daily index option implied volatility surface, 1996-2021	no page yet
Wu and Xia (2016) shadow Fed Funds rate (Atlanta Fed)	Monetary policy stance during ZLB; extends observed FFR below zero	FRED (related public source)
Taylor Rule implied rate (Bernanke 2015 blog spreadsheet)	Benchmark rate for identifying FedSupport vs non-support periods	no page yet
CRSP S&P 500 and S&P 100 index levels	Underlying prices for moneyness construction	WRDS (licensed)
Federal Reserve H15 series (effective Fed Funds rate)	Observed FFR for non-ZLB periods	FRED
Bekaert, Engstrom and Xu (2021) relative risk aversion index (nancyxu.net)	Time-varying risk aversion control and endogenous regressor	no page yet
Kansas City Fed Labor Market Conditions Index	Instrument for FedSupport and RiskAversion	FRED
FRB St. Louis Financial Stress Index	Instrument for FedSupport and RiskAversion	FRED
S&P 500 Price-Earnings Ratio	Instrument for FedSupport and RiskAversion	no page yet

Sample: 1,342 weekly observations, January 4, 1996 to December 31, 2021. Primary results on S&P 500 (SPX). Replicated on S&P 100 (OEX). 132,858 option-week observations in the multivariate regressions (Table 5, p. 11). Authors state they do not have permission to share data (Appendix B, p. 13).

When to read the full paper

Use the original if you are: testing whether the Fed Put effect extends to other derivatives markets or international indices; examining how unconventional monetary policy (QE, forward guidance) affects investor beliefs about central bank intervention; replicating the IV-GMM instrument set for options-market panel regressions with endogenous risk aversion; or extending the analysis to post-2021 data when the Fed raised rates rapidly. Tables 1-2 (pp. 8-9) document the univariate pattern and risk aversion heterogeneity; Tables 5-6 (pp. 11, 13) contain the multivariate OLS and IV-GMM estimates for pre- and post-crisis subperiods.

Attribution and rights

Source: peer-reviewed, Journal of Banking and Finance 188 (2026). This distillation was extracted by an LLM on 2026-06-25 and is not human-verified or independently reproduced. The article is paywalled (Elsevier, all rights reserved); only core results are extracted here.

Dahiya, Sandeep, Bardia Kamrad, Valerio Poti, and Akhtar Siddique. “Fed put in the equity options markets.” Journal of Banking and Finance 188 (2026) 107697. DOI: 10.1016/j.jbankfin.2026.107697. (c) 2026 Elsevier B.V. All rights reserved. Extract only; redistribution not permitted.