An Analysis of the Causal relationship between Prediction Markets and NASDAQ Volatility
Abstract
This piece investigates the high-frequency volatility of price discovery between the NASDAQ-100 Volatility Index (VXN) and NASDAQ-100 Polymarket prediction contracts. By analysing intraday data across multiple sampling frequencies (1-minute to 30-minutes), we challenge the hypothesis that prediction markets serve as an indicator of traditional equity volatility. Utilising a Vector Error Correction Model (VECM), we find evidence of a cointegrating relationship with a strictly unidirectional flow of information. The traditional market volatility (VXN) has an exogenous effect on Polymarket contracts pricing while they act as a lagging follower. Analysis of the Error Correction Term across multiple frequencies reveals severe market friction, demonstrating that retail prediction markets require an average of 105 minutes across the sampling frequencies to fully absorb real-time macroeconomic shocks priced instantly by institutional markets.
Introduction
2. Data & Variable Construction
To construct the dataset we aggregate and synchronise pricing data from the Polymarket API and Barchart.com through a python script.
First, prediction market data was sourced directly from Polymarket’s Gamma and CLOB APIs. The script actively filtered for NASDAQ-100 (‘NDX’) “up-or-down” events with a minimum trading volume of $10,000 to ensure adequate market liquidity and activity. For each identified market the start and end timestamps were converted to UTC time and 1-minute historical pricing data was extracted.
Second, high-frequency 1-minute historical data for the NASDAQ-100 Volatility Index (VXN) was aggregated from three separate CSV extracts obtained from Barchart.com. The Barchart data was provided in US Eastern Time we converted it to UTC, accounting for Daylight Saving Time ambiguities to align with the Polymarket timestamps.
Finally, the two datasets were combined using an outer merge on the 1-minute timestamps. To account for Polymarket’s sparser retail liquidity, prediction prices were forward-filled within the boundaries of each individual trading day. The script purged all overnight and weekend rows where the stock market (VXN) was closed. This resulted in the dataset used for analysis (Polymarket_10000+vol&VXN_data.csv).
To ensure validity the raw data must be transformed and synchronised. Financial time-series data at the 1-minute level is noisy and sensitive to non-trading hours.
Raw NASADAQ-100 Polymarket contract prices, that represent the probability (P) of the market ending up or down, must be mapped to the concept of volatility. I decided to use the “Uncertainty” of each Polymarket event as a proxy for volatility. The “Uncertainty” metric is defined as, ‘Uncertainty = 0.5 - |0.5 - P|’. This equation creates a metric that peaks at 0.5 (maximum uncertainty) when the contract price is 50 cents and reduces linearly to zero as the market deviates further from this value on either side.
To evaluate market dynamics across different data frequencies the tick-level data was sampled into discrete intraday intervals (1m, 3m, 5m, 10m, 15m, 30m). This aggregation was performed using a ‘ceiling_date’ alignment function. By anchoring the timestamp to the close of the interval rather than the open. This ensures that prices generated during the period are recorded exactly when they become observable. This is important as the ‘last()’ state extraction was used to replicate the standard “Close” pricing. ‘Ceiling_date’ ensures we are not aggregating our data back to a time before it was observed. The physical calendar date (Trading_Day) was extracted from the resulting buckets to establish the boundary conditions required to protect subsequent lag operators from overnight gaps.
3. Methodology
The methodology is designed to prevent spurious regression:
1. Stationarity: We first deploy the Augmented Dickey-Fuller (ADF) test to identify if the variables are stationary.
2. Optimal Memory: We utilise the Akaike Information Criterion (AIC) via VARselect on the non-stationary data to determine the market’s optimal lag memory (k).
3. Cointegration: We employ the Johansen Trace Test to determine if the markets are structurally tethered in the long-run.
4. Vector Error Correction Model (VECM) Specification: The Granger Representation Theorem states, if variables are cointegrated, standard Granger causality tests on differenced data suffer from omitted variable bias. We must construct a VECM to split causality into two dimensions, long-term equilibrium () and the short-term Error Correction Term ().
4. Empirical Results
4.1 Stationarity and Optimal Lag Memory Across Frequencies
The VXN Augmented Dickey-Fuller Tests fail to reject the null hypothesis across different frequencies, confirming that it is a non-stationary variable that wanders over time. The Uncertainty ADF tests succeed in rejecting the null hypothesis across different frequencies, suggesting that it is a stationary variable. The optimal lag parameter (k) selected by the AIC shrinks as the timestep widens, indicating that high-frequency 1-minute data requires more autoregressive memory to filter through microstructure noise than 30-minute data.
4.2 Johansen Cointegration Testing
The Johansen Trace Statistic evaluates the rank (r) of the coefficient matrix. Across our tested intervals the test statistic exceeds the 5% critical value for r=0, rejecting the null hypothesis of no cointegration. This is proof of a structural tether between the VXN and polymarket uncertainty, confirming that while the VXN and Polymarket may diverge in the short term due to localised noise, they are bound by a long-term equilibrium and cannot wander indefinitely apart.
4.3 Vector Error Correction Model (VECM) Dynamics
The core of our findings lies in the Error Correction Term (), representing the speed of adjustment. The VECM output shows the coefficient for the VXN is statistically insignificant across the intervals. This proves that VXN leads the prediction market.
Conversely the coefficient for Polymarket uncertainty is negative and highly significant. This means when the tether between the two markets is stretched it is Polymarket that must correct its price. Calculating the half-life of a shock (HL=ln(2)/||) reveals an average adjustment period across the time intervals of 105 minutes. This displays that while the institutional market reacts to macroeconomic shocks instantly, the retail prediction market reacts almost 2 hours behind.
4.4 Post-Estimation Diagnostics
To ensure model validity we test the VECM residuals. The Portmanteau test checks for serial correlation (whether past errors predict future errors), while the ARCH-LM test checks for volatility clustering.
While lower frequency buckets (15m, 30m) generally exhibit clean white-noise residuals, high-frequency intervals (1m) fail due to heavy market microstructure noise.
This shows a clear distinction in validity across time intervals. The Portmanteau test indicates that intervals from 3 to 30 minutes avoid serial correlation (p>0.05), with the 10 minute Autocorrelation Function (ACF) plot demonstrating residuals that behave almost as clean white noise. The 1-minute interval decisively fails this test (p=0.0000), seen in the ACF plot showing pronounced spikes in the VXN and significant negative autocorrelation in the Polymarket uncertainty that pass the 95% confidence bounds consistently, proving serial correlation at the micro level.
The ARCH-LM test detects volatility clustering at multiple intervals, (3-minute, 5-minute and 15-minute) marked by a p<0.05. Visualising the residuals shows distinct periods of heightened variance clustered together among periods of low variance. At the 1-minute level the Uncertainty residuals display the sparse nature of the retail prediction market order book with extended flat sequences interrupted by sharp deviations. While these ARCH effects indicate heteroskedastic error variance this is a normal characteristic of high-frequency financial data and does not bias the VECM’s long-run cointegration () coefficients.
5. Discussion & Market Microstructure Implications
The relationship is unidirectional, VXN acting on Polymarket. The highly liquid, algorithmically driven NASDAQ market anchors price discovery while Polymarket, driven by retail liquidity and manual trading, shares a long-term tether but reacts with an almost 2-hour lag. This lag suggests that arbitrage between the two markets is potentially possible if the prediction market holds sufficient volume. As prediction markets grow in volume and liquidity, we may see them become more efficient and this lag relationship close.
6. Conclusion
This VECM analysis shows that significant information only flows between these cointegrated markets from VXN to Ploymarket as it only finds statistical significance when modelling VXN as a vector autoregression of Polymarket uncertainty, proving that Polymarket uncertainty moves in a lagged order to the VXN. This proves contrary to the narrative that prediction markets serve as efficient, accurate probability models of future events, that traditional equity markets hold predictive precedence. While the wisdom of the crowd provides a sound long-term equilibrium, the microstructure of prediction markets are highly inefficient, acting as lagging sentiment aggregators of institutional volatility.
7. References
Akaike, H. (1974). A new look at the statistical model identification. IEEE Transactions on Automatic Control, 19(6), 716-723.
Dickey, D. A., & Fuller, W. A. (1979). Distribution of the estimators for autoregressive time series with a unit root. Journal of the American Statistical Association, 74(366a), 427-431.
Engle, R. F. (1982). Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation. Econometrica: Journal of the Econometric Society, 50(4), 987-1007.
Engle, R. F., & Granger, C. W. J. (1987). Co-integration and error correction: Representation, estimation, and testing. Econometrica: Journal of the Econometric Society, 55(2), 251-276.
Johansen, S. (1991). Estimation and hypothesis testing of cointegration vectors in Gaussian vector autoregressive models. Econometrica: Journal of the Econometric Society, 59(6), 1551-1580.
Ljung, G. M., & Box, G. E. P. (1978). On a measure of lack of fit in time series models. Biometrika, 65(2), 297-303.
Pfaff, B. (2008). Analysis of Integrated and Cointegrated Time Series with R (2nd ed.). Springer, New York. (Reference for the urca and vars packages).
Surowiecki, J. (2004). The Wisdom of Crowds. Doubleday.
Wickham, H., et al. (2019). Welcome to the tidyverse. Journal of Open Source Software, 4(43), 1686.