Decomposing the Variance Risk Premium, Part 2

The volatility risk premium (VRP) is the difference between implied volatility and subsequently realized volatility, and is one of the most extensively studied phenomena in options markets. We previously discussed Reference [1], which decomposes the VRP into upside and downside components and studies their dynamics separately. Reference [2] applies a similar framework to the same index, the S&P 500, but using a more recent dataset.

The author pointed out,

We examine four main points. First, we test whether investors pay a higher premium for volatility associated with equity price declines than for volatility associated with price increases. By decomposing the variance risk premium into upside and downside components using option prices and high-frequency equity return data, we find that the downside variance risk premium is statistically more pronounced than the aggregate variance risk premium.

Second, we examine whether risk premium associated with downside variance and skewness are related to the required return on equities. Empirically, these premium predict future returns, suggesting that investors view rare, large drawdowns and volatility during market declines as risk, and that compensation for bearing such risks is linked to expected equity returns.

Third, we investigate the relationship between the prediction horizon and predictive power (adjusted R2). Consistent with prior findings, predictive power for variance-related premium peaks around three to five months, while skewness-related premium exhibit relatively stronger predictive power at longer horizons.

Fourth, we evaluate whether the term structure (the difference between longer- and shorter-maturity premium) improves return forecasting. While we find limited evidence of improvement for the variance risk premium, the term structure of the skewness risk premium is statistically significant and suggests that when the longer-maturity skewness risk premium is lower (more negative) than the shorter-maturity premium, long-horizon equity returns subsequently rise, and vice versa. This is consistent with the interpretation that when investors anticipate longer-horizon tail risk, required long-run equity returns increase.

In short, the paper finds that downside VRP is substantially more pronounced than aggregate VRP. It also shows that downside variance and skewness risk premiums predict future equity returns, with variance-related predictive power strongest at medium horizons and skewness-related predictive power stronger at longer horizons. Finally, the study finds that the term structure of skewness risk premium contains forecasting information, suggesting that expectations of longer-horizon tail risk are linked to higher future required equity returns.

We believe this paper largely revisits the framework of the earlier study [1], albeit using more recent data and more extensive robustness tests, while ultimately reaching very similar conclusions.

Let us know what you think in the comments below or in the discussion forum.

References

[1] Feunou, B., Jahan-Parvar, M. R., & Okou, C. (2016), Downside Variance Risk Premium, Journal of Financial Econometrics 16 (3), 341-383

[2] Akio Ito, Variance Risk Premium, Skewness Risk Premium and Equity Expected Returns, SSRN Working Paper 6712647, 2025

Originally Published Here: Decomposing the Variance Risk Premium, Part 2

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Volatility Measures for Regime Classification

Regime detection and classification are important in portfolio management and asset allocation. One of the key inputs into regime detection models is volatility. Reference [1] examines which volatility measure is most effective for regime classification. The authors study three volatility measures,

1. Implied volatility (VIX/VIXBR),
2. GARCH conditional volatility,
3. Historical volatility.

They then incorporate them into a Hidden Markov Model framework. The paper pointed out,

The empirical evidence supports conditional volatility (GARCH as the superior proxy for regime identification in both the Brazilian and U.S. markets). Unlike implied volatility, which exhibited excessive sensitivity to short-term noise and threshold variations, the GARCH- based specification provided the greatest parameter stability and classification robustness, essential attributes for operationalizing dynamic portfolios.

A key finding of this research is the structural identification of three volatility regimes (low, medium, and high). Contrary to binary specifications often assumed in the literature for interpretability, the Bayesian Information Criterion (BIC) results demonstrated that a three-state model better captures the complex dynamics of financial markets, specifically identifying transitional phases that binary models fail to detect. This granular identification allowed for a more precise assessment of international risk transmission…

From an investment perspective, the results highlight the distinct roles of regime-based strategies. The Dynamic Regime strategy consistently outperformed the traditional Static Mean-Variance (Single Regime) strategy in risk-adjusted metrics, successfully mitigating severe drawdowns, most notably in the U.S. market, where the static strategy suffered structural losses (−18.49%) while the dynamic strategy preserved capital (+1.56%). However, the dynamic strategy did not outperform the Naive (1/N) benchmark in terms of total cumulative return…

In short, the authors conclude that GARCH conditional volatility provides the most stable and operationally reliable regime classification. Implied volatility reacts faster to market changes but produces noisier regime switching. The study also finds that a three-regime framework is superior to a simple low/high volatility classification, as the intermediate regime captures transition periods and uncertainty normalization phases.

Another important point emphasized in the paper is that regime-based strategies are best viewed as risk-management tools rather than universal return-enhancing solutions. Regime-based allocation improves drawdown control and risk-adjusted performance relative to static mean-variance optimization.

Let us know what you think in the comments below or in the discussion forum.

References

[1] Bitencourt, W. A., & Iquiapaza, R. A. (2026), Comparative analysis of volatility proxies and regime-based asset allocation, International Review of Economics and Finance, 109, 105366.

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Delta Hedging Performance Under Different Measures

Managing an option book is not trivial. There is considerable research on hedging errors, optimal hedging frequency, and the choice of volatility inputs used in hedging algorithms. Reference [1] continues this line of research by examining the effectiveness of hedging strategies under five different volatility measures:

1. Flat ATM implied volatility
2. Stochastic Volatility Inspired (SVI) implied volatility
3. Close-to-close realized volatility
4. Parkinson realized volatility
5. Yang–Zhang realized volatility.

The study uses OptionMetrics SPX options data from 2019 to 2024, including the COVID crash and the 2022 hiking cycle, and analyzes 2000 stratified options across four VIX regimes. The author pointed out,

This thesis provides the first empirical evaluation of SVI-calibrated implied volatility as a delta-hedging input on real S&P 500 index options. The results challenge three common assumptions.

First, more information does not automatically improve hedging. The SVI surface, despite encoding the full implied volatility smile with high calibration quality (median RMSE of 19.5 bps), produces 9.4% higher hedging error variance than flat ATM implied volatility. The calibration noise embedded in the five-parameter SVI fit outweighs the informational benefit of strike-specific volatilities for most option types.

Second, statistical efficiency in volatility estimation does not translate into hedging efficiency. The simple close-to-close realized volatility estimator, which uses only closing prices, outperforms both the Parkinson and Yang–Zhang estimators, which incorporate intraday range information. For hedging purposes, smoothness (low sensitivity to intraday noise) appears more valuable than efficiency (low estimation variance under GBM).

Third, and most importantly, the optimal volatility input is strongly dependent on option moneyness and market regime. SVI surface IV reduces hedging error for out-of-the-money calls by 6–12%, where the smile slope carries genuine hedgeable information. Realized volatility dominates for out-of-the-money puts, where the skew premium makes implied-based deltas biased. No single input wins everywhere, suggesting that a moneyness-conditional hedging strategy, using different volatility inputs for different regions of the option space, would outperform any static approach.

In short, the results show that, contrary to intuition, SVI surface volatility does not improve aggregate delta hedging performance. In fact, SVI increases the standard deviation of hedging errors by 9.4% relative to flat ATM implied volatility. Close-to-close realized volatility performs best overall, reducing hedging error standard deviation by 5.8%, while the Parkinson estimator performs worst. The effectiveness of volatility measures, however, is also found to depend on regime and moneyness.

Another important finding is that higher-order effects, including vanna, volga, jumps, and model misspecification, dominate hedging errors.

This paper provides valuable insights for both traders and risk managers. Let us know what you think in the comments below or in the discussion forum.

References

[1] Annigeri, Z. (2026), Regime-Dependent Delta Hedging with SVI-Calibrated Volatility Surfaces: An Empirical Analysis of SPX Index Options, Rutgers Business School, SSRN 6465741

Article Source Here: Delta Hedging Performance Under Different Measures

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Network Effects in Social Media Sentiment

Social media sentiment has become increasingly important in modern portfolio and risk management. Most studies on social media rely on aggregate sentiment measures, such as average bullishness scores or overall positive-versus-negative comment ratios. Reference [1] introduces an innovative approach to analyzing social media sentiment by investigating network effects, specifically how high-centrality users, i.e., “influencers,” affect the behavior and sentiment of regular users. The study utilizes data from the r/stocks subreddit from January 2019 to June 2022, covering approximately 3.5 million comments.

To study network effects, the authors construct a daily Reddit interaction graph in which nodes represent users and edges represent direct comment replies. They then compute eigenvector centrality to identify influential users, divide users into centrality quintiles, measure sentiment within each group, and test whether lagged sentiment from high-centrality users predicts future sentiment among lower-centrality users and the broader network. They pointed out,

In this study, we examine the relationship between online social interactions and financial markets, specifically focusing on the sentiment dissemination within a stock market community on Reddit. Our findings demonstrate that highly active users can spread their sentiments to a broader audience. This influence becomes more pronounced under two conditions: (1) when there is reduced disagreement among high-centrality nodes and (2) during periods of high market volatility. Additionally, we find that the COVID-19 pandemic represents a structural shift that enhances the influence of high-centrality nodes as increased online activity and uncertainty reshaped network dynamics…

The practical implications of our findings are twofold. For market participants, sentiment-based trading strategies can provide increased profitability, especially in commission-free trading environments. In addition, network sentiment can be an effective tool for market timing and creating downside protection. From a policy standpoint, while online networks can enhance information dissemination, the ability of a few highly active users to stimulate the beliefs of others can be exploited or, to a certain extent, can inflate the prices of specific assets in the market; one example being the GameStop short squeeze case.

In short, the results show that sentiment from influential users significantly predicts sentiment among regular users, with dissemination effects becoming stronger during the COVID period, high-volatility environments, and periods of low disagreement among influential users. The authors also develop a trading strategy based on these findings. The sentiment-timing strategy materially reduces drawdowns, while the long-only version outperforms buy-and-hold before transaction costs.

Let us know what you think in the comments below or in the discussion forum.

References

[1] Akarsu, S., & Yılmaz, N. (2026), The dynamics of online social interactions and implications on stock market returns, Journal of Economic Interaction and Coordination.

Article Source Here: Network Effects in Social Media Sentiment

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From Pinning to Amplification: Evidence from S&P500 Options

Options pinning, the tendency of underlying prices to gravitate toward strikes with concentrated open interest near expiration, is well documented. However, given the rapidly changing options landscape, it is worth reassessing whether this effect still holds.

Reference [1] examines options pinning using data from 2016 to 2025, a period marked by the proliferation of weekly and zero-days-to-expiration (0DTE) options, based on 1.6 million near-expiry SPY contracts. The author pointed out,

We find no evidence of options pinning in S&P 500 expiration dynamics across five tests on 2,294 trading days (2016–2025). The significant finding (p < 0.001) shows the opposite: high near-expiry ATM open interest is associated with wider, not narrower, daily ranges. This is consistent with the gamma amplification mechanism documented by Barbon & Buraschi (2021) and the theoretical predictions of Jeannin et al. (2008) under net short dealer gamma.

We interpret these results as evidence of a possible regime shift in S&P 500 expiration dynamics—from pinning in earlier periods (as documented by Golez & Jackwerth through 2009) to amplification in the modern era, potentially driven by the structural growth of short-dated options and changes in dealer positioning. We offer this interpretation as a hypothesis for further investigation, not as a definitive conclusion.

In short, the paper finds no evidence of pinning. Instead, on days with high open interest, prices exhibit approximately 16% wider ranges, indicating a shift from pinning to amplification. This change is likely driven by the growth of short-dated options and increased retail demand for long options, which leaves dealers short gamma and leads to larger price moves.

An interesting point discussed in the paper is that open interest is more informative than implied volatility, signifying that dealer positioning is important information.

Let us know what you think in the comments below or in the discussion forum.

References

[1] Elms, N. (2026), From Pinning to Amplification: Evidence of a Regime Shift in S&P 500 Options Expiration Dynamics, 2016–2025, SSRN 6564078

Originally Published Here: From Pinning to Amplification: Evidence from S&P500 Options

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VIX Forecasting Using Crypto Overnight Returns

Prediction is central in finance. A growing line of research uses cross-asset signals to forecast market movements. A recent example showed that Bitcoin can serve as a strong leading indicator in a machine learning-based trading system.

Along similar lines, Reference [1] examines whether cryptocurrency overnight returns, defined as price changes during U.S. equity market closures, can predict the VIX. For this study, the authors use five-minute data of Bitcoin and Ethereum from 2018 to 2025, motivated by the idea that crypto markets are highly sensitive to sentiment, and that overnight returns capture this information. They pointed out,

This study examines the informational content of cryptocurrency returns through a novel temporal decomposition framework that aligns cryptocurrency trading activity with U.S. equity market hours. Our analysis shows that the overnight returns of both Bitcoin and Ethereum capture a distinct dimension of investor sentiment, which significantly improves the predictability of equity market volatility…

We then explore the predictive power of cryptocurrency overnight returns for VIX dynamics. In-sample analysis reveals a significantly negative relationship between cryptocurrency overnight returns and subsequent trading-hour VIX changes, indicating that positive overnight sentiment predicts a reduction in equity market uncertainty during the following trading session. Out-of-sample analysis demonstrates that models incorporating cryptocurrency overnight returns consistently outperform baseline models, with results remaining robust across subperiods and extending to other U.S. implied volatility indices. The economic significance of these findings is further validated through long-short trading strategies in VIX derivatives, where overnight-return-augmented models generate superior performance across different risk-aversion levels.

In short, the results show that crypto overnight returns have a negative predictive relationship with the VIX, with strong in-sample and out-of-sample performance. A trading strategy based on this signal is found to be profitable, and the results hold across different periods, including COVID and non-COVID regimes, and extend to other volatility indices.

Once again, the study reinforces the role of cryptocurrencies as leading indicators for broader market dynamics.

Let us know what you think in the comments below or in the discussion forum.

References

[1] Gu, M., Lin, J., & Liu, S. (2026), Beyond Conventional Sentiment Indicators: Cryptocurrency’s Hidden Potential in VIX Forecasting, Economic Modelling.

Post Source Here: VIX Forecasting Using Crypto Overnight Returns

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