Category: options trading strategies

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.

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.

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.

The breakdown of the volatility risk premium into overnight and intraday sessions is an active and emerging area of research. It holds not only academic interest but also practical implications. ETF issuers are launching new ETFs to capitalize on the overnight risk premium, and the shift toward around-the-clock trading could impact the VRP and popular strategies such as covered call writing. In this post, I’ll discuss the VRP breakdown, its implications, impact, and more.

Volatility Risk Premium is a Reward for Bearing Overnight Risk

The volatility risk premium (VRP) represents the difference between the implied volatility of options and the realized volatility of the underlying asset. Reference [1] examines the asymmetry in the VRP. Specifically, it investigates the VRP during the day and overnight sessions. The research was conducted in the Nifty options market, but previous studies in the S&P 500 market reached the same conclusion.

Findings

– There is a significant difference in returns between overnight and intraday short option positions, unrelated to a weekend effect.

– The return asymmetry decreases as option moneyness and maturity increase.

– A systematic relationship exists between day-night option returns and the option Greeks.

– Average post-noon returns are significantly negative for short call positions and positive for short put positions, while pre-noon returns are largely insignificant, indicating that the VRP varies throughout the trading day for calls and puts.

– A significant jump in the underlying index reduces the day-night disparity in option returns due to increased implied volatilities, which boost both intraday and overnight returns.

– Strong positive overnight returns suggest that the VRP in Nifty options prices mainly compensates for overnight risk.

– A strategy of selling index options at the end of the trading day and covering them at the beginning of the next day yields positive returns before transaction costs but is not profitable after accounting for transaction costs.

Reference

[1] Aparna Bhat, Piyush Pandey, S. V. D. Nageswara Rao, The asymmetry in day and night option returns: Evidence from an emerging market, J Futures Markets, 2024, 1–18

Inventory Risk and Its Impact on the Volatility Risk Premium

The previous paper suggests that the VRP is specifically a reward for bearing overnight risk. Reference [2] goes further by attempting to answer why this is the case. It provides an explanation in terms of market makers’ inventory risks, as they hold a net-short position in put options.

Findings

-Put option risk premia are significantly negative overnight when equity exchanges are closed and continuous delta-hedging is not feasible.

-Intraday, when markets are liquid and delta-hedging is possible, put option risk premia align with the risk-free rate.

-Call options show no significant risk premia during the sample period.

-Market makers’ short positions in puts expose them to overnight equity price “gap” risks, while their call option positions are more balanced between long and short, resulting in minimal exposure to gap risk.

-Increased overnight liquidity reduces option risk premia. Regulatory changes and the acquisition of major electronic communication networks in 2006 boosted overnight equity trade volumes from Monday to Friday, reducing the magnitude of weekday option risk premia compared to weekend risk premia.

-The study concludes that the S&P 500 option risk premium arises from a combination of options demand and overnight equity illiquidity.

An interesting implication of this research is that the introduction of around-the-clock trading could potentially reduce the VRP.

Reference

[2] J Terstegge, Intermediary Option Pricing, 2024, Copenhagen Business School

Closing Thoughts

Understanding the breakdown of the volatility risk premium into overnight and intraday components is crucial for both researchers and practitioners. As ETF issuers develop products to leverage the overnight risk premium and markets move toward 24-hour trading, these dynamics could significantly impact volatility strategies. Recognizing these shifts can help investors refine their approaches and adapt to evolving market conditions.

Tail risk hedging aims to protect portfolios from extreme market downturns by using strategies such as out-of-the-money options or volatility products. While effective in mitigating large losses, the challenge lies in balancing cost and long-term returns. In this post, we’ll discuss tail risk hedging and whether it can be done at a reasonable cost.

Tail Risk Hedging Strategies: Are They Effective?

Tail risk hedging involves purchasing put options to protect the portfolio either partially or fully. Reference [1] presents a study of different tail risk hedging strategies. It explores the effectiveness of put option monetization strategies in protecting equity portfolios and enhancing returns.

Findings

– Eight different monetization strategies were applied using S&P 500 put options and the S&P 500 Total Return index from 1996 to 2020.

– Results compared against an unhedged index position and a constant volatility strategy on the same underlying index.

– Tail risk hedging, in this study, yielded inferior results in terms of risk-adjusted and total returns compared to an unhedged index position.

– Over a 25-year period, all strategies’ total returns and Sharpe ratios were worse than the unhedged position.

– Buying puts involves paying for the volatility risk premium, contributing to less favorable results.

– The results are sensitive to choices of time to expiry and moneyness of purchased options in tested strategies.

– The authors suggest the possibility of minimizing hedging costs by optimizing for strikes and maturities.

Reference:

[1] C.V. Bendiksby, MOJ. Eriksson, Tail-Risk Hedging An Empirical Study, Copenhagen Business School

How Can Put Options Be Used in Tail Risk Hedging?

The effectiveness of using put options to hedge the tail risks depends on the cost of acquiring put options, which can eat into investment returns. Reference [2] proposes a mixed risk-return optimization framework for selecting long put options to hedge S&P 500 tail risk. It constructs hypothetical portfolios that continuously roll put options for a tractable formulation.

Findings

– The article discusses the effectiveness of tail risk hedging. It highlights that the premium paid for put options can be substantial, especially when continuously renewing them to maintain protection. This cost can significantly impact investment returns and overall portfolio performance.

– The article introduces an optimization-based approach to tail-risk hedging, using dynamic programming with variance and CVaR as risk measures. This approach involves constructing portfolios that constantly roll over put options, providing protection without losing significant long-term returns.

– Contrary to previous research, the article suggests that an effective tail-risk hedging strategy can be designed using this optimization-based approach, potentially overcoming the drawbacks of traditional protective put strategies.

-The proposed hedging strategy overcame traditional drawbacks of protective put strategies. It outperforms both direct investments in the S&P 500 and static long put option positions.

Reference

[2] Yuehuan He and Roy Kwon, Optimization-based tail risk hedging of the S&P 500 index, THE ENGINEERING ECONOMIST, 2023

Closing Thoughts

Tail risk hedging is expensive. While the first paper demonstrated that tail risk hedging leads to inferior returns, it suggested that results could be improved by optimizing strike prices and maturities. The second paper built on this idea and proposed a hedging scheme based on optimization. The proposed strategy outperforms both direct investments in the S&P 500 and static long put option positions.

Financial models and strategies are usually universal and can be applied across different asset classes. However, in some cases, they must be adapted to the unique characteristics of the underlying asset. In this post, I’m going to discuss option pricing models and trading strategies in commodities, specifically in the crude oil market.

Volatility Smile in the Commodity Market

Paper [1] investigates the volatility smile in the crude oil market and demonstrates how it differs from the smile observed in the equity market.  It proposes to use the new method developed by Carr and Wu in order to study the volatility smile of commodities. Specifically, the authors examine the volatility smile of the United States Oil ETF, USO.

Findings

– This paper examines the information derived from the no-arbitrage Carr and Wu formula within a new option pricing framework in the USO (United States Oil Fund) options market.

– The study investigates the predictability of this information in forecasting future USO returns.

– Using the no-arbitrage formula, risk-neutral variance, and covariance estimates are obtained under the new framework.

– The research identifies the term structure and dynamics of these risk-neutral estimates.

– The findings reveal a “U”-shaped implied volatility smile with a positive curvature in the USO options market.

Usually, an equity index such S&P 500 exhibits a downward-sloping implied volatility pattern, i.e. a negative implied volatility skew. Oil, on the other hand, possesses a different volatility smile. This is because while equities are typically associated with crash risks, oil prices exhibit both sharp spikes and crashes, leading to a different implied volatility pattern. This highlights the importance of considering the specific characteristics and dynamics of different asset classes when analyzing and interpreting implied volatility patterns.

Reference

[1] Xiaolan Jia, Xinfeng Ruan, Jin E. Zhang, Carr and Wu’s (2020) framework in the oil ETF option market, Journal of Commodity Markets, Volume 31, September 2023, 100334

Statistical Arbitrage in the Crude Oil Markets

Reference [2] directly applies statistical arbitrage techniques, commonly used in equity markets, to the crude oil market.  It utilizes cointegration to construct a statistical arbitrage portfolio. Various methods are then used to test for stationarity and mean reversion: the Quandt likelihood ratio (QLR), augmented Dickey-Fuller (ADF) test, autocorrelations, and the variance ratio. The constructed strategy performed well both in- and out-of-sample.

Findings

– This paper introduces the concept of statistical arbitrage through a trading strategy known as the mispricing portfolio.

– It focuses specifically on mean-reverting strategies designed to exploit persistent anomalies observed in financial markets.

– Empirical evidence is presented to demonstrate the effectiveness of statistical arbitrage in the crude oil markets.

– The mispricing portfolio is constructed using cointegration regression, establishing long-term pricing relationships between WTI crude oil futures and a replication portfolio composed of Brent and Dubai crude oils.

-Mispricing dynamics revert to equilibrium with predictable behaviour. Trading rules, which are commonly used in equity markets, are then applied to the crude oil market to exploit this pattern.

Reference

[2] Viviana Fanelli, Mean-Reverting Statistical Arbitrage Strategies in Crude Oil Markets, Risks 2024, 12, 106.

Closing Thoughts

As we’ve seen, techniques and models utilized in the equity market can sometimes be applied directly to the crude oil market, while other times they need to be adapted to the unique characteristics of the crude oil market. In any case, strong domain knowledge is essential.

Educational Video

In this webinar, Quantitative Trading in the Oil Market, Dr Ilia Bouchouev delivers an interesting and insightful presentation on algorithmic trading in the oil market. He also encourages viewers to apply the techniques discussed for the oil market to other markets, such as equities.