options trading strategies – Relative Value Arbitrage

Volatility vs. Volatility of Volatility: Conceptual and Practical Differences

Volatility and volatility of volatility are highly correlated and share many similar characteristics. However, there are subtle but important differences between them. In this post, we will examine some of these differences and explore an application of volatility of volatility in portfolio management.

Improving Portfolio Management with Volatility of Volatility

Managing portfolios using volatility has proven effective. Reference [1] builds on this research by proposing the use of volatility of volatility for portfolio management. The rationale behind using volatility of volatility is that it represents uncertainty.

Unlike risk, which refers to situations where future returns are unknown but follow a known distribution, uncertainty means that both the outcome and the distribution are unknown. Stocks may exhibit uncertainty when volatility or other return distribution characteristics vary unpredictably over time.

Practically, the author used a stock’s daily high and low prices to derive its volatility of volatility.

Findings

-The study investigates how volatility-managed investment strategies perform under different levels of uncertainty across stocks and over time.

-A new measure of volatility-of-volatility (vol-of-vol) is introduced as a proxy for uncertainty about risk, capturing a unique dimension distinct from traditional volatility.

-Results show that abnormal returns from volatility management are concentrated in stocks with low uncertainty and during periods of low aggregate uncertainty.

-The effectiveness of sentiment-based explanations for volatility-managed returns is conditional on the level of uncertainty.

-Cross-sectional differences in uncertainty help explain why volatility-managed factor portfolios perform unevenly across stocks and time.

-Theoretical analysis extends a biased belief model, showing that higher vol-of-vol reduces volatility predictability and belief persistence, weakening the benefits of volatility timing.

-The study hypothesizes that volatility management is most effective for low-uncertainty stocks and in low-uncertainty market environments.

-Empirical tests use realized vol-of-vol derived from intraday high and low prices as the measure of uncertainty.

-Consistent with prior literature, uncertainty is positively related to future returns and contains unique predictive information not explained by other stock characteristics.

-Volatility management significantly improves risk-adjusted performance in low-uncertainty stocks and during low aggregate uncertainty periods, while uncertainty also helps explain performance variation across asset pricing factor portfolios.

In short, using the volatility of volatility as a filter proves to be effective, particularly for low-uncertainty stocks.

We find it insightful that the author distinguishes between risk and uncertainty and utilizes the volatility of volatility to represent uncertainty.

Reference

[1] Harris, Richard D. F. and Li, Nan and Taylor, Nicholas, The Impact of Uncertainty on Volatility-Managed Investment Strategies (2024), SSRN 4951893

Beyond volatility of volatility

This section is written by Alpha in Academia

The Volatility of Volatility Index (VVIX) is a composite measure, driven by both short-term market panic and long-term risk expectations.

For years, the VVIX, often dubbed the “fear of fear” index, was treated primarily as a measure of the volatility of volatility (VOV), but new research reveals it contains a second, equally critical component: Long-Run Variance (LRV).

Using a sophisticated model and leveraging a novel technique involving risk-neutral cumulant data extracted from VIX options, researchers decomposed the VVIX dynamics. Their analysis reveals that the factors driving the index change dramatically depending on market conditions. Specifically, the short-term panic measure, VOV, significantly contributes only during acute periods of financial distress, which aligns with intuition. However, during stable or bull markets, the VVIX is primarily driven by the LRV component, reflecting persistent, underlying risk expectations.

In fact, when testing the explanatory power on market-neutral straddle portfolios using S&P 500 options, combining LRV and VOV produced an adjusted explanatory power up to three times greater than baseline models. The finding shows that the index provides “a clear answer to the question of the informational content of the VVIX, showing that it reflects not only the VOV but also an additional important component—the LRV”. Investors should thus view the VVIX not just as a fear gauge, but as a dual-sensor monitoring immediate market stress and long-term risk.

Reference

[2] Bacon, Étienne and Bégin, Jean-François and Gauthier, Geneviève, Beyond volatility of volatility: Decomposing the informational content of VVIX, 2025, SSRN 5611090

Closing Thoughts

In summary, both studies emphasize the role of volatility-of-volatility in understanding risk and market behavior. The first shows that volatility management is most effective in low-uncertainty environments, while the second reveals that the VVIX reflects not only short-term market stress but also long-term risk expectations. Together, they suggest that volatility-of-volatility offers deeper insight into both portfolio performance and the broader dynamics of market uncertainty.

Effectiveness of Covered Call Strategy in Developed and Emerging Markets

Covered call strategies are often promoted as an income-generation tool for investors seeking steady returns with reduced risk. But how effective are they in practice? In this post, we take a closer look at their real-world performance across different markets.

Do Covered Calls Deliver Superior Returns?

The covered call strategy is a popular and conservative options trading approach. It involves an investor holding a long position in an underlying asset, typically a stock, and then selling call options on that asset. These call options provide the buyer with the right to purchase the underlying asset at a predetermined strike price within a specific timeframe. By selling these calls, the investor generates additional income through the premiums received.

While the covered call strategy provides an additional income, it caps potential profits if the asset’s price rises significantly. Covered calls are often employed by investors seeking income while holding a moderately bullish view of the underlying asset’s price. It can be an effective way to enhance returns and manage risk in a portfolio.

The investment management industry has actively promoted the covered call strategy. But in reality, does it deliver superior returns compared to the buy-and-hold approach? Reference [1] effectively examined this question.

Findings

-The study evaluates the performance of a covered call strategy relative to the SPY ETF benchmark over the period from July 2009 to April 2023.

-Three covered call variations are analyzed: at-the-money (ATM), two percent out-of-the-money (OTM), and five percent OTM call options.

-The results show no statistically significant difference between the covered call strategies and the benchmark in terms of overall performance.

-Among the tested strategies, the five percent OTM covered call achieved the highest annualized return of 16%, followed by the two percent OTM with 15%, compared to SPY’s 13%.

-The study cautions investors that these figures do not account for taxes, transaction costs, or implementation expenses, which could reduce the strategy’s real-world profitability.

-The analysis distinguishes between two major market periods — the COVID-19 pandemic and the Russia–Ukraine conflict — to evaluate performance consistency.

-The findings suggest that while covered call strategies may offer comparable or slightly better returns in some conditions, their advantage is not statistically robust.

-The thesis excludes mean-variance ratios due to potential biases caused by the negatively skewed return distribution of covered call strategies.

-The results imply that covered call strategies may be better suited for specific market environments rather than as a general outperforming strategy.

Overall, the study highlights the limited evidence supporting the superiority of covered call strategies over a simple buy-and-hold approach for ETFs.

Reference

[1] Tomáš Ježo, Effect of covered calls on portfolio performance, 2023, Charles University

Do Covered Calls Deliver Superior Returns – Emerging Markets

The previous paper discussed the risk-adjusted returns of the covered call strategy in the US market. Reference [2] further studied the profitability of the covered call strategy in international markets.

Findings

-The study evaluates the effect of call writing on ETF portfolio returns and risk, focusing on the Indian capital market.

-Results indicate that adding call writing to ETFs generally reduces returns and increases risk compared to holding ETFs alone.

-Exceptions occur for portfolios using deep out-of-the-money (OTM) options—specifically OTM5 and OTM7—which achieved higher returns but also significantly higher risk.

-The OTM5 portfolio showed a 47% gain in rupee terms and 27% as a percentage of investment, though its risk nearly doubled.

-The high volatility of options often leads to sharp losses, with the potential to erase a year’s gains in a single week of negative returns.

-ETFs, while index-based, do not perfectly track their benchmarks, contributing to deviations in portfolio performance.

-The higher return of the OTM5 portfolio is attributed to a 68% success rate, suggesting potential benefits if the strategy is applied consistently over the long term.

-The findings support the idea that covered call strategies can generate income and manage risk if applied using deep OTM options and maintained for extended periods.

-The study aligns with prior research indicating that covered call strategies underperform in bull markets but can reduce risk or outperform in neutral or declining markets.

In brief, in the Indian market, covered calls yield lower returns with higher risks (as measured by portfolio volatility). The exception is when selling far out-of-the-money call options, but even then, the risk-adjusted returns remain lower due to the higher volatility of returns. This result is consistent with the result in the US market.

Reference

[2] Dr. Abhishek Shahu1, Dr. Himanshu Tiwari, Dr. Mahesh Joshi, Dr. Sanjay Kavishwar, An Analysis of the Effectiveness of Index ETFS and Index Derivatives in Covered Call Strategy, Journal of Informatics Education and Research, Vol 4 Issue 3 (2024)

Closing Thoughts

Both studies assess covered call strategies and reach broadly consistent conclusions. The U.S. study finds only marginal performance improvements over buy-and-hold, while the emerging market study shows potential for higher returns using deep out-of-the-money options but at increased risk. Overall, covered calls may enhance income under specific market conditions, though their benefits remain limited and context-dependent.

Tail Risk Hedging Using Option Signals and Bond ETFs

Tail risk hedging plays a critical role in portfolio management. I discussed this topic in a previous article. In this post, I continue the discussion by presenting different techniques for managing tail risks.

Hedging with Puts: Do Volatility and Skew Signals Work?

Portfolio hedging remains a complex and challenging task. A straightforward method to hedge an equity portfolio is to buy put options. However, this approach comes at a cost—the option premiums—leading to performance drag. As a result, many research studies are focused on designing effective hedging strategies that offer protection while minimizing costs.

Reference [1] presents the latest research in this area. It examines hedging schemes for equity portfolios using several signals, including MOM (momentum), TREND, HVOL (historical volatility), IVOL (implied volatility), and SKEW. The study also introduces a more refined rehedging strategy for put options:

-If, during the investment period, a put option’s delta falls to −0.9 or lower, the option is sold to lock in profits and avoid losing them in case of a sudden price reversal.

-Put options are bought when implied volatility is below 10%, as they are considered cheap. No position is taken if implied volatility is above 30%, to avoid overpaying for expensive options.

Findings

-The study investigates how option strategies can be integrated into equity portfolios to improve performance under risk constraints. It highlights weaknesses in traditional equity and fixed-income diversification for institutional investors.

-The research tests backward-looking signals from equity markets and forward-looking signals from options markets in covered call and protective put strategies.

-The TREND signal is found to be the most valuable, reducing portfolio risk without reducing returns compared to equity-only portfolios.

-The SKEW signal has a positive impact on GMV allocation but is less effective under EW allocation.

-Adding extra trading rules (TR1, TR2) does not enhance performance and is often negative.

-Backtests of long-put strategies confirm that the TREND signal offers the best balance between downside protection and performance preservation.

-Bootstrapped results diverge from backtests, showing that HVOL and IVOL signals outperform the BASE portfolio in risk-adjusted terms.

-The differences between bootstrap and backtest results suggest that the effectiveness of signals depends on the prevailing market regime.

In short, buying put options using the TREND signal appears to improve portfolio risk-adjusted returns. While SKEW and IVOL add little in backtests, they perform better in bootstrapped results, suggesting that the effectiveness of put protection strategies is regime-dependent.

This study offers a comprehensive evaluation of various hedging rules. There is no conclusive answer yet, implying that designing an efficient hedging strategy is complex and requires ongoing effort. Still, the article is a strong step in the right direction.

Reference

[1] Sylvestre Blanc, Emmanuel Fragnière, Francesc Naya, and Nils S. Tuchschmid, Option Strategies and Market Signals: Do They Add Value to Equity Portfolios?, FinTech 2025, 4(2), 25

Tail Risk Hedging with Corporate Bond ETFs

Reference [2] proposed a tail risk hedging scheme by shorting corporate bonds. Specifically, it constructed three signals—Momentum, Liquidity, and Credit—that can be used in combination to signal entries and exits into short high-yield ETF positions to hedge a bond portfolio.

Findings

-Investment Grade (IG) bonds in the US typically trade at modest spreads over Treasuries, reflecting corporate default risk.

-During market crises, IG spreads widen and liquidity decreases due to rising credit risk and forced selling by asset holders such as mutual funds.

-This non-linear widening of spreads during drawdowns is referred to as downside convexity, which can be captured through short positions in IG ETFs.

-The study develops three signals—Momentum, Liquidity, and Credit—to time entry and exit for short IG positions as a dynamic hedge.

-The dynamic hedge effectively protects high-carry bond funds like PIMIX and avoids drawdowns for funds such as DODIX, even after considering trading and funding costs.

-Each signal captures different aspects of the IG bond market, and their combination provides the strongest results, improving the Sortino ratio by at least 0.7.

-The hedge model performs consistently well across a broad range of tested parameters, showing robustness.

-Shorting IG (LQD) and HY (HYG) ETFs is found to be more cost-effective than shorting individual IG bonds, due to liquidity and low bid-ask spreads.

-IG and HY CDXs, despite larger volumes, lack the downside convexity of ETFs and are less effective for hedging.

Overall, ETF-based hedging delivers both cost efficiency and strong downside protection, making it a practical approach for institutional investors.

An interesting insight from this paper is that it points out how using corporate ETFs benefits from downside convexity, while using credit default swaps, such as IG CDXs, does not.

Reference

[2] Travis Cable, Amir Mani, Wei Qi, Georgios Sotiropoulos and Yiyuan Xiong, On the Efficacy of Shorting Corporate Bonds as a Tail Risk Hedging Solution, arXiv:2504.06289

Closing Thoughts

Both studies highlight the importance of adapting traditional portfolio strategies by incorporating alternative approaches to better manage risk and improve performance. The first paper shows how option-based overlays, particularly when guided by signals such as trend, can enhance equity portfolios by providing downside protection without materially reducing returns. The second paper demonstrates that credit and liquidity risks in investment-grade bonds can be more effectively managed through dynamic hedging with liquid bond ETFs. Together, these findings underscore that integrating derivative-based strategies offers investors practical tools to navigate market volatility, reduce drawdowns, and achieve more resilient portfolio outcomes.

Stochastic Volatility Models for Capturing ETF Dynamics and Option Term Structures

The standard Black-Scholes-Merton model is valuable in both theory and practice. However, in certain situations, more advanced models are preferable. In this post, I explore stochastic volatility models.

Stock and Volatility Simulation: A Comparative Study of Stochastic Models

Stochastic volatility models, unlike constant volatility models, which assume a fixed level of volatility, allow volatility to change. By incorporating factors like mean reversion and volatility of volatility, stochastic volatility models offer a robust framework for pricing derivatives, managing risks, and improving investment strategies.

Reference [1] investigates several stochastic models for simulating stock and volatility paths that can be used in stress testing and scenario analysis. It also proposes a method for evaluating these stochastic models. The models studied include

-Geometric Brownian Motion (GBM),

-Generalized Autoregressive Conditional Heteroskedasticity (GARCH),

-Heston stochastic volatility,

-Stochastic Volatility with Jumps (SVJD), and a novel

-Multi-Scale Volatility with Jumps (MSVJ).

Findings

-The paper compares several stochastic models for simulating leveraged ETF (LETF) price paths, using TQQQ as the case study.

-The MSVJ model captures both fast and slow volatility components and demonstrates superior performance in modeling volatility dynamics and price range estimation.

-The evaluation framework tests price and volatility characteristics against actual TQQQ data under different market conditions, including the COVID-19 crash and the 2022 drawdown.

-GBM and Heston models are most effective in simulating market crashes, as they reproduce historical drawdowns and capture tail risk well.

-The MSVJ model is the most suitable for option pricing because it provides the best fit for both price and volatility, as measured by its highest WMCR.

-The SVJD model performs best in generating realistic price and volatility paths, as it incorporates both stochastic volatility and jump processes.

-SVJD’s realism makes it useful for portfolio managers in backtesting trading strategies and assessing portfolio risk across different market conditions.

In short, each model has distinct strengths, so the optimal choice depends on whether the goal is risk management, option pricing, or portfolio simulation.

Reference

[1] Kartikay Goyle, Comparative analysis of stochastic models for simulating leveraged ETF price paths, Journal of Mathematics and Modeling in Finance (JMMF) Vol. 5, No. 1, Winter & Spring 2025

Modeling Short-term Implied Volatilities in Heston Model

Despite their advantages, stochastic volatility models have difficulty in accurately characterizing both the flatness of long-term implied volatility (IV) curves and the steep curvature of short-term ones. Reference [2] addresses this issue by introducing a term-structure-based correction to the volatility of volatility (vol-vol) term in the classical Heston stochastic volatility model.

Findings

-Existing financial models struggle to capture implied volatility (IV) shapes across all option maturities simultaneously. This paper introduces a term-structure-based correction to the volatility of volatility (vol-vol) term in the classical Heston stochastic volatility model.

-The correction is modeled as an exponential increase function of the option expiry.

-An approximate formula for IV is derived using the perturbation method and applied to Shanghai Stock Exchange 50 ETF options.

-Numerical and empirical results show that the correction significantly improves the Heston model’s ability to capture short-term IVs.

-The corrected model enhances both IV forecasting and option quoting performance compared to the classical Heston model.

-While demonstrated on the Heston model, the method can be extended to other stochastic volatility models.

-Future research could include embedding strike into the correction function to better capture the entire implied volatility surface.

In brief, both short- and long-term IVs are accurately modeled in the new Heston variant.

This paper improves the existing Heston model. Thus, it helps portfolio managers and risk managers to better manage the risks of investment portfolios.

Reference

[2] Youfa Sun, Yishan Gong, Xinyuan Wang & Caiyan Liu, A novel term-structure-based Heston model for implied volatility surface, International Journal of Computer Mathematics, 1–24.

Closing Thoughts

Both studies advance volatility modeling in financial markets. The first highlights how different stochastic models, including a novel multi-scale volatility with jumps framework, can better simulate leveraged ETF dynamics under varying conditions, with specific strengths depending on the application. The second shows that enhancing the Heston model with a term-structure correction improves the fit of implied volatility surfaces across maturities, especially for short-dated options. Together, these findings underscore the importance of refining volatility models to capture market complexity and improve applications in risk management, option pricing, and forecasting.

Predictive Information of Options Volume in Equity Markets

A lot of research in options literature has been devoted to the volatility risk premia and developing advanced pricing models. Much less attention has been given to volume. In this post, I’ll discuss some aspects of options volume.

Can Options Volume Predict Market Returns?

Most of the research in equity and index options has been devoted to volatility and the volatility risk premium. Relatively less attention is paid to options volume.

Reference [1] examined options volume from the perspective of in-the-money options order imbalance.

Findings

-The public directional order imbalance of S&P500 in-the-money options reliably predicts negative market returns over monthly horizons extending up to three months.

-Predictability from DOI remains significant even after controlling for established sentiment indicators, volatility indexes, and various macroeconomic uncertainty measures.

-In-the-money options are largely insensitive to VIX fluctuations, making DOI a clearer measure of investors’ directional market sentiment.

-Findings show DOI maintains predictive strength up to nine months, with long-term persistence explained by the limits-to-arbitrage framework.

-The negative predictive power of DOI primarily comes from public customers, not firm proprietary traders, revealing differences in institutional decision-making quality.

-Evidence suggests that mutual funds and pension funds, often assumed to be highly sophisticated, sometimes make suboptimal choices reflected in ITM options trading.

-DOI has no predictive influence across broader financial asset classes, making its forecasting power specific to equity index returns.

-High-tech industry stocks appear most sensitive to DOI, reinforcing connections between sentiment-driven trading and sector-specific return predictability.

-Predictability of DOI strengthens during recessionary periods, highlighting how sentiment effects intensify when markets face heightened uncertainty and tighter arbitrage opportunities.

In conclusion, the study demonstrates that in-the-money options volume, particularly public directional order imbalance, provides valuable insight into investor sentiment and market dynamics, offering strong predictive power for future returns, especially during recessionary periods and under limits-to-arbitrage conditions.

Reference

[1] Wang, Li, and Ni, Sophie Xiaoyan and Stouraitis, Aristotelis, Index Options Trading and Sentiment (2021). SSRN 3981994

Option Volume Imbalance Is a Predictor of Market Returns

The previous article showed that options volume is a predictor of future market returns. On a similar topic, Reference [2] examined the Option Volume Imbalance (OVI) and its relationship with the future prices of the underlying assets. The authors utilized data from the PHLX exchange to conduct research.

Findings

-The study highlighted Option Volume Imbalance as a useful feature that helps forecast future equity returns with measurable predictive power.

-Using PHLX exchange data, researchers analyzed OVI signals across multiple market participant groups, uncovering significant differences in predictive accuracy.

-Market Makers’ OVI produced the strongest results, achieving annualized Sharpe Ratios up to 4.5, even under simple betting frameworks excluding costs.

-Extreme OVI signals, grouped into tail portfolios, generated daily profits reaching 4 basis points depending on the portfolio sizing strategy employed.

-Evidence showed Customer and Broker OVIs carried some predictive value, but Firm Proprietary trades and Professional Customers offered no meaningful signals.

-Performance improvements emerged when analyzing OVI magnitude, with second to fourth quantile ranking groups consistently outperforming other quantile groupings.

-Stronger predictive signals originated from option contracts with high implied volatility compared to contracts with relatively lower implied volatility levels.

-Put option volumes were more informative than call volumes, suggesting downside-oriented trades carry greater predictive content in equity markets.

-Overall, the study demonstrated that OVI effectively predicts overnight excess market returns, particularly when driven by Market Maker activity.

In short, the authors showed that the Option Volume Imbalance has predictive power on directional overnight price movements for the underlyings. They also demonstrated that the Option Volume Imbalance from high implied volatility contracts is significantly more informative than options contracts with low implied volatility.

Reference

[2] Michael, Nikolas, and Cucuringu, Mihai, and Howison, Sam, Option volume imbalance as a predictor for equity returns (2022).

Closing Thoughts

Overall, the research on options volume and order imbalances provides strong evidence that these measures contain valuable predictive information. Whether through DOI in in-the-money options or OVI across participant groups, the findings reveal consistent links between sentiment, volatility, and returns.

These papers contribute to the body of research that focuses on the predictive power of options volume. The research could open the door to further studies that examine option volumes from different data sets and at different time frames.

Behavioral Biases and Retail Options Trading

Behavioral finance is important, but it’s not often discussed in quantitative trading. In this post, I explore some aspects of behavioral finance.

Why Do Investors Lose Money?

Behavioral finance is the study of how financial behavior affects economic decisions and market outcomes, and how those decisions and outcomes are affected by psychological, social, and cultural factors.

Behavioral finance research has shown that people do not always make rational decisions when it comes to money. Factors such as emotion, social pressure, and cognitive biases can all lead to suboptimal decisions. Reference [1] lists mistakes made by investors:

Findings

-Investors often fail to diversify adequately, exposing themselves to unnecessary idiosyncratic risk, which results in lower overall returns that could be avoided with simple diversification strategies.

-Many investors underperform the mutual funds they invest in due to poor timing decisions, such as buying high and selling low, which diminishes the benefits of professional fund management.

-The disposition effect leads investors to sell winning investments too early while holding onto losing ones for too long, negatively impacting portfolio performance over time.

-Investors who pay insufficient attention to markets or their portfolios tend to earn lower returns compared to more engaged and informed peers.

-Investment behavior is often reactive; individuals increase market exposure following strong returns and reduce it after losses, leading to suboptimal timing and missed opportunities.

-Home bias is prevalent among investors, who prefer local stocks despite lacking superior information about them, resulting in poor diversification and reduced portfolio efficiency.

-Overconfidence causes investors to trade excessively, and data shows that high-frequency traders typically earn worse returns than those who trade less frequently.

-Herd behavior is common, with investors often buying or selling the same stocks simultaneously, which amplifies market inefficiencies and can harm returns.

-Many investors chase past performance, moving their money into funds that have recently performed well, often too late to benefit from continued outperformance.

-Despite the availability of lower-cost options, investors frequently allocate funds to expensive products, ignoring predictable performance characteristics and reducing overall investment efficiency.

In summary, the article is a good primer on behavioral finance. It discusses, in particular, the investment mistakes that cause investors to lose money.

Reference

[1] Firth, Chris, An Introduction to Investment Mistakes (2015). SSRN 2609989

Retail Options Traders’ Behavior

Retail investors are individual, non-professional investors who buy and sell securities, such as stocks, options, and mutual funds, for their accounts rather than for an organization or institution. Unlike institutional investors, who manage large sums of money on behalf of clients or large entities, retail investors typically trade in smaller quantities and often use online brokerage accounts to facilitate their transactions.

A considerable amount of research has been devoted to studying retail investors’ behavior. A recent paper by the CBOE [2] utilizes the exchange’s data and refutes some academic research findings.

Findings

-Retail investor participation in the options market increased notably from 18% to 31% between the fourth quarter of 2019 and the fourth quarter of 2023.

-Complex orders made up 58% to 76% of retail open positions, challenging the belief that retail traders primarily hold simple long positions.

-Academic studies often miss complex retail trading activity due to reliance on limited datasets or assumptions that overlook retail investor sophistication.

-Retail traders show a wider range of strategies than previously thought, including multi-leg options trades and hedging techniques, indicating greater versatility.

-The study found that the assumption that retail investors lack sophistication is outdated, as many use advanced tools and approaches for managing risk.

-Market maker order imbalance in SPX options declined from -14% in December 2016 to -12% in May 2023, even with increased use of 0DTE options.

-This decline in imbalance suggests the growth of 0DTE SPX options has not disrupted market maker order flow, contrary to popular belief.

-When SPX options are excluded, retail trading still represented 32% to 40% of all non-SPX options traded on the C1 exchange by notional value.

-The use of CBOE’s internal data offers a more accurate and complete view of retail investor behavior compared to earlier studies relying on proxies.

-Overall, the findings indicate retail investors are more active, strategic, and integral to the options market than traditional views have assumed.

This research by the CBOE, using more complete data, sheds light on the behavior of retail options traders. It provides more insight into the changing dynamics of the options markets.

Reference

[2] Selina Han, Unveiling the Sophistication: Understanding Retail Investors’ Trading Behavior in the U.S. Options Market, May 2024, CBOE

Closing Thoughts

In summary, the first article serves as a solid introduction to behavioral finance, focusing on the common mistakes that lead to investor losses. The second article presents CBOE research that, using more complete data, offers a clearer view of retail options trading behavior and the evolving structure of the options market.

The Calendar Effects in Volatility Risk Premium

I recently covered calendar anomalies in the stock markets. Interestingly, patterns over time also appear in the volatility space. In this post, I’ll discuss the seasonality of volatility risk premium (VRP) in more detail.

Breaking Down the Volatility Risk Premium: Overnight vs. Intraday Returns

The decomposition of the volatility risk premium (VRP) into overnight and intraday components is an active area of research. Most studies indicate that the VRP serves as compensation for investors bearing overnight risks.

Reference [1] continues this line of research, with its main contribution being the decomposition of the variance risk premium into overnight and intraday components using a variance swap approach. The study also tests the predictive ability of these components and examines the seasonality (day-of-week effects) of the VRP.

An interesting finding of the paper is the day-of-week seasonality. For instance, going long volatility at the open and closing the position at the close tends to be profitable on most days, except Fridays.

Findings

-The analysis is conducted on implied variance stock indices across the US, Europe, and Asia.

-Results show that the VRP switches signs between overnight and intraday periods—negative overnight and positive intraday.

-The findings suggest that the negative VRP observed in previous studies is primarily driven by the overnight component.

-The study evaluates the predictive power of both intraday and overnight VRP in forecasting future equity returns.

-The intraday VRP component captures short-term risk and demonstrates predictive ability over 1–3-month horizons.

-The overnight VRP component reflects longer-term risk and shows predictive power over 6–12-month horizons.

Reference

[1] Papagelis, Lucas and Dotsis, George, The Variance Risk Premium Over Trading and Non-Trading Periods (2024), SSRN 4954623

Volatility Risk Premium Seasonality Across Calendar Months

Reference [2] examines the VRP in terms of months of the year. It concluded that the VRP is greatest in December and smallest in October.

An explanation for the large VRP in December is that during the holiday season, firms might refrain from releasing material information, leading to low trading volumes. The combination of low trading volume and the absence of important news releases would result in lower realized volatility.

Findings

-The paper identifies a “December effect” in option returns, where delta-hedged returns on stock and S&P 500 index options are significantly lower in December than in other months.

-This effect is attributed to investors overvaluing options at the start of December due to underestimating the typically low volatility that occurs in the second half of the month.

– The reduced volatility is linked to lighter stock trading during the Christmas holiday season.

– A trading strategy that involves shorting straddles at the beginning of December and closing the position at the end of the month yields a hedged return of 13.09%, with a t-value of 6.70.

-This return is much higher than the unconditional sample mean of 0.88%, highlighting the strength of the effect.

The paper is the first in academic literature to document and analyze this specific December anomaly in option markets. It is another important contribution to the understanding of the VRP.

Reference

[2] Wei, Jason and Choy, Siu Kai and Zhang, Huiping, December Effect in Option Returns (2025). SSRN 5121679

Closing Thoughts

In this post, I have discussed volatility patterns in terms of both days of the week and months of the year. Understanding this seasonality is crucial for traders and portfolio managers, as it can inform better timing of volatility trades and risk management strategies.

Profitability of Dispersion Trading in Liquid and Less Liquid Environments

Dispersion trading is an investment strategy used to capitalize on discrepancies in volatilities between an index and its constituents. In this issue, I will feature dispersion trading strategies and discuss their profitability.

Profitability of a Dispersion Trading Strategy

Reference [1] provided an empirical analysis of a dispersion trading strategy to verify its profitability. The return of the dispersion trading strategy was 23.51% per year compared to the 9.71% return of the S&P 100 index during the same period. The Sharpe ratio of the dispersion trading strategy was 2.47, and the portfolio PnL had a low correlation (0.0372) with the S&P 100 index.

Findings

-The article reviews the theoretical foundation of dispersion trading and frames it as an arbitrage strategy based on the mispricing of index options due to overestimated implied correlations among the index’s constituents.

-The overpricing phenomenon is attributed to the correlation risk premium hypothesis and the market inefficiency hypothesis.

-Empirical evidence shows that a basic dispersion trading strategy—using at-the-money straddles on the S&P 100 and a representative subset of its stocks—has significantly outperformed the broader stock market.

-The performance of the dispersion strategy demonstrated a very low correlation to the S&P 100 index, highlighting its diversification potential.

-This study reinforces the idea that sophisticated options strategies can uncover persistent market inefficiencies.

This article proved the viability of the dispersion trading strategy. However, there exist two issues related to execution,

-The analysis assumes no transaction costs, which is a key limitation; in practice, only market makers might replicate the back-tested performance due to the absence of slippage.

-Another limitation is the simplified delta hedging method used, which was based on daily rebalancing.

-A more optimized hedging approach could potentially yield higher returns and partially offset transaction costs.

Reference

[1] P. Ferrari, G. Poy, and G. Abate, Dispersion trading: an empirical analysis on the S&P 100 options, Investment Management and Financial Innovations, Volume 16, Issue 1, 2019

Dispersion Trading in a Less Liquid Market

The previous paper highlights some limitations of the dispersion strategy. Reference [2] further explores issues regarding liquidity. It investigates the profitability of dispersion trading in the Swedish market.

Findings

-Dispersion trading offers a precise and potentially profitable approach to hedging vega risk, which relates to volatility exposure.

-The strategy tested involves shorting OMXS30 index volatility and taking a long volatility position in a tracking portfolio to maintain a net vega of zero.

-The backtesting results show that vega risk can be accurately hedged using dispersion trading.

– Without transaction costs, the strategy yields positive results.

-However, after accounting for the bid-ask spread, the strategy did not prove to be profitable over the simulated period.

– High returns are offset by substantial transaction costs due to daily recalibration of tracking portfolio weights.

– Less frequent rebalancing reduces transaction costs but may result in a worse hedge and lower correlation to the index.

In short, the study concluded that if we use the mid-price, then dispersion trading is profitable. However, when considering transaction costs and the B/A spreads, the strategy becomes less profitable.

I agree with the author that the strategy can be improved by hedging less frequently. However, this will lead to an increase in PnL variance. But we note that this does not necessarily result in a smaller expected return.

Reference

[2] Albin Irell Fridlund and Johanna Heberlei, Dispersion Trading: A Way to Hedge Vega Risk in Index Options, 2023, KTH Royal Institute of Technology

Closing Thoughts

I have discussed the profitability of dispersion strategies in both liquid and illiquid markets. There exist “inefficiencies” that can be exploited, but doing so requires a more developed hedging approach and solid infrastructure. The “edge” is apparent, but consistently extracting it demands a high level of skill, discipline, and operational capability. In reality, it is this latter part, i.e. the ability to build and maintain the necessary infrastructure, that represents the true edge.

Breaking Down Volatility: Diffusive vs. Jump Components

Implied volatility is an important concept in finance and trading. In this post, I further discuss its breakdown into diffusive volatility and jump risk components.

Decomposing Implied Volatility: Diffusive and Jump Risks

Implied volatility is an estimation of the future volatility of a security’s price. It is calculated using an option-pricing model, such as the Black-Scholes-Merton model.

Reference [1] proposed a method for decomposing implied volatility into two components: a volatility component and a jump component. The volatility component is the price of a portfolio only bearing volatility risks and the jump component is the price of a portfolio only bearing jump risks. The decomposition is made by constructing two option portfolios: a delta- and gamma-neutral but vega-positive portfolio and a delta- and vega-neutral but gamma-positive portfolio. These portfolios bear volatility and jump risks respectively.

Findings

– The study examines the return patterns of straddles and their component portfolios, focusing on jump risk and volatility risk around earnings announcements.

– The findings show that straddle returns closely resemble those of the jump risk portfolio, suggesting that the options market prioritizes earnings jump risk during these events.

– The research highlights the significant role of earnings jump risk in financial markets, as it is substantially priced into straddles and influences both options and stock market behavior.

– A proposed straddle price decomposition method and the S-jump measure could be applied to other market events, such as M & A and natural disasters, to assess risk and pricing dynamics.

This paper discussed an important concept in option pricing theory; that is, the implied volatilities, especially those of short-dated options, comprise not only volatility but also jump risks.

Reference

[1] Chen, Bei and Gan, Quan and Vasquez, Aurelio, Anticipating Jumps: Decomposition of Straddle Price (2022). Journal of Banking and Finance, Volume 149, April 2023, 106755

Measuring Jump Risks in Short-Dated Option Volatility

Unlike long-dated options, short-dated options incorporate not only diffusive volatility but also jump risks. One of the earliest works examining the jump risks is by Carr et al [2].

Reference [3] developed a stochastic jump volatility model that includes jumps in the underlying asset. It then constructed a skew index, a so-called crash index.

Findings

-This paper introduces a novel methodology to measure forward-looking crash risk implied by option prices, using a tractable stochastic volatility jump (SVJ) model.

-The approach isolates the jump size component from the stochastic volatility embedded within uncertainty risk, extending beyond the Black-Scholes-Merton framework.

-The methodology parallels the construction of implied volatility surfaces, enabling the development of an option-implied crash-risk curve (CIX).

-The CIX is strongly correlated with non-parametric option-implied skewness but offers a more refined measure of crash risk by adjusting for stochastic volatility (Vt) and emphasizing tail risk dynamics.

-In contrast, option-implied skewness reflects both crash and stochastic volatility risks, presenting smoother characteristics of the risk-neutral density.

-Empirical analysis reveals a notable upward trend in the CIX after the 2008 financial crisis, aligning with narratives on rare-event risks and emphasizing the value of incorporating such beliefs into asset pricing frameworks.

References

[2] P Carr, L Wu, What type of process underlies options? A simple robust test, The Journal of Finance, 2003

[3] Gao, Junxiong and Pan, Jun, Option-Implied Crash Index, 2024. SSRN

Closing Thoughts

In this issue, I discussed the breakdown of volatility into diffusive and jump components. Understanding this distinction is important for trading, and risk management in theory and practice.

Capturing Volatility Risk Premium Using Butterfly Option Strategies

The volatility risk premium is a well-researched topic in the literature. However, less attention has been given to specific techniques for capturing it. In this post, I’ll highlight strategies for harvesting the volatility risk premium.

Long-Term Strategies for Harvesting Volatility Risk Premium

Reference [1] discusses long-term trading strategies for harvesting the volatility risk premium in financial markets. The authors emphasize the unique characteristics of the volatility risk premium factor and propose trading strategies to exploit it, specifically for long-term investors.

Findings

– Volatility risk premium is a well-known phenomenon in financial markets.

– Strategies designed for volatility risk premium harvesting exhibit similar risk/return characteristics. They lead to a steady rise in equity but may suffer occasional significant losses. They’re not suitable for long-term investors or investment funds with less frequent trading.

– The paper examines various volatility risk premium strategies, including straddles, butterfly spreads, strangles, condors, delta-hedged calls, delta-hedged puts, and variance swaps.

– Empirical study focuses on the S&P 500 index options market. Variance strategies show substantial differences in risk and return compared to other factor strategies.

– They are positively correlated with the market and consistently earn premiums over the study period. They are vulnerable to extreme stock market crashes but have the potential for quick recovery.

– The authors conclude that volatility risk premium is distinct from other factors, making it worthwhile to implement trading strategies to harvest it.

Reference

[1] Dörries, Julian and Korn, Olaf and Power, Gabriel, How Should the Long-term Investor Harvest Variance Risk Premiums? The Journal of Portfolio Management 50 (6) 122 – 142, 2024

Trading Butterfly Option Positions: a Long/Short Approach

A butterfly option position is an option structure that requires a combination of calls and/or puts with three different strike prices of the same maturity. Reference [2] proposes a novel trading scheme based on butterflies’ premium.

Findings

– The study calculates the rolling correlation between the Cboe Volatility Index (VIX) and butterfly options prices across different strikes for each S&P 500 stock.

– The butterfly option exhibiting the strongest positive correlation with the VIX is identified as the butterfly implied return (BIR), indicating the stock’s expected return during a future market crash.

– Implementing a long-short strategy based on BIR allows for hedging against market downturns while generating an annualized alpha ranging from 3.4% to 4.7%.

-Analysis using the demand system approach shows that hedge funds favor stocks with a high BIR, while households typically take the opposite position.

-The strategy experiences negative returns at the bottom of a market crash, making it highly correlated with the pricing kernel of a representative household.

-The value-weighted average BIR across all stocks represents the butterfly implied return of the market (BIRM), which gauges the severity of a future market crash.

-BIRM has a strong impact on both the theory-based equity risk premium (negatively) and the survey-based expected return (positively).

This paper offers an interesting perspective on volatility trading. Usually, in a relative-value volatility arbitrage strategy, implied volatilities are used to assess the rich/cheapness of options positions. Here the authors utilized directly the option positions premium to evaluate their relative values.

Reference

[2] Wu, Di and Yang, Lihai, Butterfly Implied Returns, SSRN 3880815

Closing Thoughts

In summary, both papers explore strategies for capturing the volatility risk premium. The first paper highlights the distinct characteristics of the volatility risk premium and outlines trading strategies tailored for long-term investors. The second paper introduces an innovative trading scheme centered around butterfly option structures. Together, these studies contribute valuable insights into optimizing risk-adjusted returns through strategic volatility trading.