Draft:Information-Implied Volatility

Information-implied volatility (IIV) is a proposed measure of expected return variability derived from the statistical properties of non-price information, including news flow, macroeconomic announcements, corporate disclosures, and alternative datasets. Unlike realized volatility, which is based on historical price fluctuations, or implied volatility, which is inferred from options markets, information-implied volatility conditions return uncertainty on informational inputs alone. The concept is related to established research in Bayesian learning, market microstructure, and the mixture-of-distributions hypothesis.^[1]

Definition

Information-implied volatility is defined as the conditional variance of future returns given an information set ${\displaystyle {\mathcal {I}}_{t}}$:

${\displaystyle \sigma _{{\text{IIV}},t}^{2}=\operatorname {Var} (R_{t+1}\mid {\mathcal {I}}_{t})}$

The information set may include macroeconomic data, textual sentiment indicators, regulatory announcements, alternative data, or firm-specific disclosures. This perspective follows Bayesian models in financial economics in which market participants update expectations in response to new information.^[2]

Bayesian Framework

A standard formulation begins with a Gaussian prior for future returns:

${\displaystyle R\sim {\mathcal {N}}(\mu _{0},\sigma _{0}^{2})}$

Each new information item ${\displaystyle I_{i}}$ is modeled as a likelihood with mean ${\displaystyle \mu _{i}}$ and variance ${\displaystyle \sigma _{i}^{2}}$. Under Bayesian precision weighting, the posterior variance is:

${\displaystyle \sigma _{\text{post}}^{2}=\left({\frac {1}{\sigma _{0}^{2}}}+\sum _{i=1}^{n}{\frac {1}{\sigma _{i}^{2}}}\right)^{-1}}$

Information-implied volatility is the posterior variance:

${\displaystyle \sigma _{\text{IIV}}^{2}=\sigma _{\text{post}}^{2}}$

Bayesian learning frameworks are widely used in macro-finance and asset pricing research.^[3]

Regime-Switching and Mixture Models

To represent asymmetric or heavy-tailed informational effects, mixture-of-normals or regime-switching models may be used:

${\displaystyle p(R_{t+1}\mid {\mathcal {I}}_{t})=\sum _{k=1}^{K}w_{k}({\mathcal {I}}_{t})\,{\mathcal {N}}(\mu _{k},\sigma _{k}^{2})}$

The mixture variance is:

${\displaystyle \sigma _{\text{IIV}}^{2}=\sum _{k}w_{k}(\sigma _{k}^{2}+\mu _{k}^{2})-\left(\sum _{k}w_{k}\mu _{k}\right)^{2}}$

Such models are well-established in econometrics for representing regime-dependent return dynamics.^[4][5]

Information Arrival and Volatility

The relationship between volatility and information arrival has been studied extensively in market microstructure. Clark introduced a subordinated process in which volatility is proportional to the rate of information flow.^[6]

Tauchen and Pitts related trading volume to information arrival, formalizing the mixture-of-distributions hypothesis.^[7]

High-frequency research has documented volatility responses to macroeconomic announcements.^[8]

Information-implied volatility generalizes these findings by conditioning variance directly on informational variables.

Construction Methods

Textual and News-Based Inputs

Natural language processing methods extract sentiment, topic relevance, and novelty from textual sources such as regulatory filings or news reports.^[9]

Macroeconomic Surprise Models

Macroeconomic data surprises may be standardized relative to forecasting errors:

${\displaystyle I_{\text{macro}}={\frac {{\text{Actual}}-{\text{Forecast}}}{\text{Historical Std}}}}$

Such measures are widely used in research on exchange rates and fixed-income markets.^[10]

Alternative Data

Alternative information sources may include satellite imagery, mobility metrics, web traffic patterns, and supply-chain indicators. These sources often provide early insights into firm- or sector-specific developments.

Conflict and Dispersion Measures

Information-implied volatility may incorporate measures of disagreement or heterogeneity across signals:

${\displaystyle \sigma _{\text{IIV}}^{2}=\sigma _{\text{post}}^{2}+\lambda \cdot \operatorname {Conflict} ({\mathcal {I}}_{t})}$

where ${\displaystyle \lambda }$ is an empirically calibrated parameter.

Relation to Other Volatility Measures

Information-implied volatility differs from:

• Realized volatility: historical price-based variation
• Implied volatility: expectations inferred from option prices
• Conditional volatility: models such as GARCH relying on return history

Empirical work finds that information variables often improve volatility forecasts when combined with return-based models.^[11]

Applications

Applications of IIV may include:

• early identification of informational stress
• volatility forecasting
• event studies
• quantitative trading
• portfolio allocation under information-conditioned uncertainty

Limitations

• absence of standardized methodology
• sensitivity to modeling choices
• large data and computational requirements
• potential difficulty isolating pure information effects
• reliance on quality and relevance of input datasets

See also

• Implied volatility
• Realized volatility
• Market microstructure
• Bayesian econometrics
• News analytics

Category:Financial economics Category:Volatility

References

1. Veronesi, Pietro (2000). "How Does Information Quality Affect Stock Returns?". Journal of Finance. 55 (2): 807–837. doi:10.1111/0022-1082.00229.
2. Pastor, Lubos; Veronesi, Pietro (2003). "Stock Valuation and Learning About Profitability". Journal of Finance. 58 (5): 1749–1789. doi:10.1046/j.1540-6261.2003.00683.x.
3. Pastor, Lubos; Veronesi, Pietro (2009). Aït-Sahalia, Yacine; Hansen, Lars (eds.). Learning in Financial Markets. Elsevier. {{cite book}}: Unknown parameter |booktitle= ignored (help)
4. Hamilton, James D. (1989). "A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle". Econometrica. 57 (2): 357–384. doi:10.2307/1912559.
5. Kim, Chang-Jin; Nelson, Charles (1999). State-Space Models with Regime Switching. MIT Press.
6. Clark, Peter K. (1973). "A Subordinated Stochastic Process Model with Finite Variance for Speculative Prices". Econometrica. 41 (1): 135–155. doi:10.2307/1913889.
7. Tauchen, George; Pitts, Mark (1983). "The Price Variability–Volume Relationship on Speculative Markets". Econometrica. 51 (2): 485–505. doi:10.2307/1912002.
8. Andersen, Torben G.; Bollerslev, Tim (1998). "Deutsche Mark–Dollar Volatility: Intraday Activity Patterns, Macroeconomic Announcements, and Longer Run Dependencies". Journal of Finance. 53 (1): 219–265. doi:10.1111/0022-1082.215229.
9. Loughran, Tim; McDonald, Bill (2011). "When Is a Liability Not a Liability? Textual Analysis, Dictionaries, and 10-Ks". Journal of Finance. 66 (1): 35–65. doi:10.1111/j.1540-6261.2010.01625.x.
10. Jansen, David W.; de Haan, Jakob (2003). "Statements of ECB Officials and Their Effect on the Euro–Dollar Exchange Rate". Journal of International Money and Finance. 22 (4): 369–387. doi:10.1016/S0261-5606(03)00013-2.
11. Engle, Robert F.; Ng, Victor (1993). "Measuring and Testing the Impact of News on Volatility". Journal of Finance. 48 (5): 1749–1778. doi:10.1111/j.1540-6261.1993.tb05127.x.