Volatility in Prediction Markets: A Structural Approach

Abstract: Forward-looking volatility forecasts are central inputs to derivatives pricing, market making, risk management, and volatility-linked trading strategies, with ARCH and GARCH models serving as the canonical workhorses. Such models are natural in standard asset markets, where prices are positive-valued stochastic processes and volatility is typically inferred from return dynamics. Prediction markets have a different structure: prices are bounded probabilities, payoffs are binary, and contracts resolve at known deadlines. We develop and estimate a volatility model tailored to binary prediction markets. The model combines two economic mechanisms: a Wright-Fisher deadline-resolution component, capturing how remaining binary uncertainty is forced to resolve over time, and a Glosten-Milgrom order-flow component, capturing volatility from informed trading as reflected in spreads and volume. Using a large panel of Kalshi contracts, we show that these structural variables carry substantial forecasting power. Plain ARCH/GARCH benchmarks are dominated by structural specifications; combining the structural model with residual GARCH dynamics gives the best overall forecasts. The model also provides an interpretable measurement framework: volatility is highest near fifty-fifty prices, rises near resolution, and varies across categories with the timing and discreteness of information arrival. Economics contracts are closer to smooth deadline-resolution dynamics, while sports contracts exhibit more event-concentrated, jump-like behavior. Across major categories, category-specific fitting does not systematically improve out-of-sample performance, suggesting that the structural specification transfers beyond the pooled headline result.

• The paper introduces a dual-channel model that decomposes prediction market volatility into deadline-resolution and adverse-selection components.
• It demonstrates that the DR-AS model reduces forecast error by 34% compared to traditional ARCH/GARCH benchmarks using extensive empirical data.
• Key implications include enhanced risk management and market microstructure insights across diverse event categories.

Volatility in Prediction Markets: A Structural Approach

Introduction

"Volatility in Prediction Markets: A Structural Approach" (2607.08199) addresses the challenge of forecasting forward-looking volatility in binary prediction markets. Unlike traditional asset markets, where models such as ARCH/GARCH are the canonical tools for volatility forecasting, prediction markets present a fundamentally different structure—prices represent probabilities, outcomes are binary, and resolution occurs at known deadlines. This paper develops and empirically validates a dual-channel, structural volatility model that leverages characteristics unique to prediction markets, such as bounded price dynamics and deadline-driven information resolution, combined with microstructural features reflecting informed trading.

Structural Model: Deadline-Resolution and Order-Flow Channels

The proposed model decomposes the conditional variance of a prediction market’s probability price into two orthogonal components:

1. Wright-Fisher Deadline-Resolution (DR) Channel: Captures the release of binary uncertainty ($p_t(1-p_t)$) over the remaining time to resolution ($\tau_t$), enforcing the requirement that all uncertainty must be resolved by the terminal time.
2. Glosten-Milgrom Adverse-Selection (AS) Channel: Models volatility arising from informed trading, parameterized by the joint dynamics of bid-ask spreads ($s_t$) and trading volume ($V_t$). This component is scaled by a monotonic transformation of trading volume and reflects microstructure-driven price uncertainty.

The joint model (DR-AS) expresses per-hour conditional variance as:

$$h_t^2 = \frac{p_t(1-p_t)}{\tau_t} + K \cdot \nu(V_t) \frac{s_t^2}{4}$$

where $K$ is an estimated parameter and $\nu(V_t)$ is an empirically selected activity proxy (with concave forms such as $\sqrt{V_t}$ favored by the results).

Figure 1: Price $p$. Maximum over minimum realized volatility ratio is $59.2\times$, reflecting the core boundary convexity of $\tau_t$0 in realized volatility.

Empirical Evaluation and Numerical Results

The empirical strategy utilizes an extensive panel of over 880,000 hourly binary-option contract observations from Kalshi, spanning multiple years and event categories. The evaluation metric is the volume-weighted Winkler interval score (VW-IS) for next-hour price forecast intervals, which directly penalizes both overly wide and insufficiently sharp volatility estimates.

Key findings include:

• ARCH/GARCH Benchmarks: Plain ARCH(1) and GARCH(1,1) models are substantially outperformed by all structural specifications. Specifically, the closed-form DR-AS model (with $\tau_t$1) reduces VW-IS by 34% relative to GARCH(1,1).
• Deadline-Resolution Channel: The $\tau_t$2 term already yields a nontrivial improvement over probit-Brownian alternatives and non-structural models, highlighting the significance of contract resolution deadlines and binary payoff structure.
• Order-Flow Channel: The inclusion of the joint spread-activity term ($\tau_t$3) further reduces forecast error, especially in regimes characterized by high microstructural volatility.

Importantly, the most accurate overall forecasts are provided by hybrid models—GARCH+DR-AS—demonstrating that while structural components dominate, residual volatility clustering is present and best modeled additively.

Figure 2: The DR-AS model’s forecast error decomposed by price $\tau_t$4, highlighting outperformance over plain GARCH at high-uncertainty regions ($\tau_t$5).

Category Heterogeneity and Model Portability

The predictive utility of the DR-AS model is robust across a variety of event categories (Sports, Politics, Economics, Entertainment, etc.). Notably, the same global model specification suffices; refitting parameters on a per-category basis typically does not improve out-of-sample performance, indicating strong structural portability.

Nevertheless, pronounced heterogeneity in volatility regimes exists:

• Economics Markets ("Smooth" Environment): Volatility is well-explained by the DR channel alone, reflecting gradual belief updating as information approaches the deadline (e.g., scheduled macroeconomic data releases).
• Sports Markets ("Event-Concentrated" Environment): Large and abrupt volatility spikes associated with discrete game events (e.g., goals, injuries) concentrate a disproportionate share of trading volume. Although the DR-AS model remains best-in-class, the fit is notably worse, indicating the potential additive value of explicit jump/event-clock extensions.

Figure 3: Global fit versus per-category fit, by category. Portability of parameter estimates is confirmed across major categories—refitting provides negligible or negative improvements.

Microstructure Diagnostics and Stylized Facts

Model-free binning highlights empirically that:

• Volatility is maximized at central probabilities ($\tau_t$6) and decays sharply at boundaries, conforming to the $\tau_t$7 functional form (see Figure 1).
• Time-to-resolution is a strong, monotonic driver ($\tau_t$8 max/min bin change).
• While bid-ask spreads and volume are weaker univariate drivers, their joint effect is significant through the adverse-selection channel.

These empirical diagnostics are consistent with the theoretical decomposition and justifies the model’s functional architecture.

Figure 4: Within-category VW-IS by specification, showing consistency of DR-AS performance across event types.

Implications and Future Directions

From an applied perspective, the structural model delivers interpretable, robust, and substantially superior volatility forecasts for probability prices, with direct applications to risk management, derivatives pricing, market making, and policy analysis leveraging real-time prediction-market data.

On the theoretical side, the paper articulates that naive importation of asset-return volatility dynamics into the prediction-market domain is deeply suboptimal—volatility is fundamentally shaped by the binary boundary, deadline-driven information resolution, and microstructural realities of modern order books.

Open directions for future research include:

• Integrating deadline and order-flow channels via explicit covariance terms to capture correlated public/private information shocks
• Modeling the update/no-update process jointly with conditional volatility
• Extending the framework with explicit jump/event-clock components for event-concentrated markets; such approaches may further enhance fit in sports or other heterogeneous event environments

Figure 5: Price $\tau_t$9 shows the nonlinearity and boundary compression of realized volatility near $s_t$0 and $s_t$1, confirming the structural form.

Conclusion

"Volatility in Prediction Markets: A Structural Approach" demonstrates that the unique structure of prediction markets necessitates specialized volatility modeling. Imposing the correct process-level and microstructural constraints provides substantial improvements over traditional financial econometric approaches, and these gains generalize across substantial categorical heterogeneity. The dual-channel DR-AS model provides a practical and theoretically justified blueprint for future work, suggesting a productive direction for empirical finance, market microstructure, and probabilistic information aggregation research.