Inventory Risk and Its Impact on the Volatility Risk Premium

The volatility risk premium (VRP) is the difference between the implied volatility of options and the realized volatility of the underlying asset, representing the compensation investors earn for taking on volatility risk.

Recent research suggests that the VRP is specifically a reward for bearing overnight risk. Reference [1] goes further by attempting to answer why this is the case. It provides an explanation in terms of market makers' inventory risks. The authors pointed out,

This paper suggests that S&P 500 option risk premia largely result from the combination of options demand and overnight equity illiquidity, which expose risk-averse intermediaries to unhedgeable inventory risk. I show that S&P 500 option risk premia are on average insignificant intraday, but significantly negative overnight, outside of regular exchange trading hours. Dealers’ inventory exposure to overnight equity price gaps can explain this finding. Dealers have a net-short position in put options, which exposes them to overnight equity “gap risk”, the risk that equity prices change overnight, since overnight equity liquidity is too low for continuous delta-hedging. In contrast, intraday equity liquidity presents few such obstacles. Supporting this channel, the emergence of overnight equity trading around 2006 leads to a relative reduction in option risk premia over parts of the week that include more overnight trading sessions, suggesting a causal effect of equity liquidity on option risk premia, likely through dealers’ inventory risk.

In summary, the article concluded that,

• 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.
• Dealers' 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.

An interesting implication of this research is that the introduction of around-the-clock trading could potentially reduce the VRP, as increased liquidity and continuous trading would mitigate overnight risk exposure for market participants.

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

References

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

Originally Published Here: Inventory Risk and Its Impact on the Volatility Risk Premium

source https://harbourfronts.com/inventory-risk-impact-volatility-risk-premium/

Does Trend Following Still Work on Single-Name Stocks? Updated Results

In a paper published in 2005, Wilcox et al. [1] showed that trend following worked on single-name stocks. Twenty years later, they retested the methodology using new, survivorship bias-free data [2].

Basically, the trading system works as follows:

• Entry: If, at the close of day t, a stock meets the price and liquidity filters, and its closing price equals or exceeds the highest adjusted close in its history, a buy order is placed at the open on day t + 1.
• Exit: At the close of day t, a trailing stop level is calculated using the Average True Range (ATR). This trailing stop is updated daily but never lowered. If, at the close of day t, the stock’s price falls below the trailing stop level, a sell order is executed at the open on day t + 1.

The authors pointed out,

This study highlights the sustained potential of long-only trend-following strategies applied to U.S. equities, building on and extending the foundational research of Wilcox and Crittenden [1]. By analyzing over 75 years of data and more than 66,000 trades, the paper confirms the profitability of trend-following systems, driven by a small number of outsized winners that compensate for more frequent, smaller losses. The strategy’s ability to thrive in various market conditions underscores its robustness, even in the face of evolving market dynamics.

In summary, even after 20 years, the original method remains profitable. However, under realistic conditions, transaction costs made it impractical, particularly for small accounts. To address this issue, the authors implemented a cost-saving mechanism to manage transaction costs. As a result, after accounting for transaction costs, small accounts became more profitable.

…While the theoretical model demonstrates exceptional performance, with a compound annual growth rate (CAGR) of 15.02%, an annualized alpha of 6.19%, and a maximum drawdown of 31.75%, the practical implementation of this strategy is challenged by high turnover and transaction costs. These obstacles, particularly impactful for smaller portfolios, were addressed by introducing a Turnover Control mechanism, which significantly enhances cost-efficiency and ensures alignment with theoretical results.

We believe the results are commendable, but we note a highly skewed profit distribution, with less than 7% of trades driving cumulative profitability. This makes it challenging for a small account to select the right stocks to trade profitably.

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

References

[1] C. Wilcox, & E. Crittenden, Does Trend-Following Work on Stocks? The Technical Analyst, 14, 1-19, 2005

[2] Zarattini, Carlo and Pagani, Alberto and Wilcox, Cole, Does Trend-Following Still Work on Stocks? 2025. https://ift.tt/nsdToXM

Originally Published Here: Does Trend Following Still Work on Single-Name Stocks? Updated Results

source https://harbourfronts.com/trend-following-still-work-single-name-stocks-updated-results/

Examining ITM Options Among Retail and Professional Traders

A significant amount of research has focused on at-the-money (ATM) and out-of-the-money (OTM) options due to their liquidity and leverage effects. However, little attention has been given to in-the-money (ITM) options.

Reference [1] addresses this gap by studying ITM options, particularly in the context of retail traders. The author pointed out,

This study fills the gap by highlighting the economic significance of ITM options and examining the behavioral and economic factors that influence investor preferences for these lower-leverage instruments. ITM options, particularly those with short maturities, have become increasingly popular with retail investors due to their perceived higher probability of payoff and the potential for consistent, albeit smaller, returns. By constructing one of the most comprehensive open-close option databases, covering 70% of the equity options market, I provide new insights into the trading behaviors of small customers, who drive much of the ITM options activity.

Among the findings, I observe that ITM options capture a significantly larger share of the dollar volume traded by small customers, especially in large-cap stocks and short-term contracts. Retail investors, as evidenced by social media data from StockTwits, are particularly drawn to ITM call options during periods of heightened retail attention, often focusing on high-priced technology stocks. This trend persists even when controlling for stock returns, volatility, and news volume, suggesting that social media plays a critical role in shaping retail trading behavior.

In summary, the key findings are:

• ITM options deliver more stable returns, reinforcing the idea that retail investors are attracted to their higher probability of generating positive returns in short-term strategies.
• The average dollar volume of ITM options exceeds that of OTM options for trades made by small customers. This trend is less noticeable for options traded by professionals and firms.
• Small customers trade a higher dollar volume of ITM options for maturities of less than seven days.
• The dollar volume of ITM call options traded by small customers is predominantly concentrated in large-cap technology stocks.

This is an interesting study. We believe that ITM options can be beneficial not only for retail traders but also for professionals.

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

References

[1] Edna Lopez Avila, In the Money? Low-Leverage in the time of Option Betting, 2025, MIT

Originally Published Here: Examining ITM Options Among Retail and Professional Traders

source https://harbourfronts.com/examining-itm-options-among-retail-professional-traders/

Measuring Jump Risks in Short-Dated Option Volatility

Unlike long-dated options, short-dated options incorporate not only diffusive volatility but also jump risks. The commonly used VIX and SKEW indices cannot clearly identify the jump risk component in options volatility. To better isolate and present the jump risk component, Reference [2] developed a stochastic jump volatility model that includes jumps in the underlying asset. The authors pointed out,

In this paper, we have pioneered a methodology to gauge forward-looking crash risk as implied from option prices. Utilizing the tractable SVJ model, this parametric approach isolates the jump size component from the stochastic volatility encapsulated within uncertainty risk. Our method extends beyond the traditional Black-Scholes model, paralleling the construction of the implied volatility surface and facilitating the creation of an option-implied crash-risk curve ...

Our method’s efficacy is underscored by its strong correlation with non-parametric option-implied skewness. Nevertheless, we have crafted our CIX as a nuanced measure of crash risk, designed to adjust for the influence of V_t, and illuminate the tail risk aspects of asset pricing dynamics. In juxtaposition, option-implied skewness is reliant on both crash and stochastic volatility risks and epitomizes the more smooth characteristics of the risk-neutral density.

Empirically, we uncover an intriguing upward trend in CIX following the 2008 financial crisis.This finding is well supported by narratives about rare events in news coverage, highlighting the importance of incorporating beliefs about rare events within a theoretical framework.

In short, the author utilized this new framework and calculated a skew index, referred to as a Crash Index, to represent the jump component. This index is highly correlated with the traditional SKEW index, and they also uncovered an interesting upward trend in the Crash Index following the 2008 financial crisis.

This is not the first paper to address jump risks in short-dated options, but its key contribution lies in the construction of a skew index. To the best of our knowledge, one of the earliest works in this area is by Carr et al. [2]

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

References

[1] Gao, Junxiong and Pan, Jun, Option-Implied Crash Index (2024). https://ift.tt/3DKGvnw

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

Originally Published Here: Measuring Jump Risks in Short-Dated Option Volatility

source https://harbourfronts.com/measuring-jump-risks-short-dated-option-volatility/

Formal Study of Overfitting in Trading System Design

Trading systems often experience performance deterioration after going live, largely due to overfitting. Reference [1] formally studied this issue, using analytical approximations for the in-sample and out-of-sample Sharpe ratios of portfolios. The authors pointed out,

This paper derives analytical approximations for the in-sample and out-of-sample Sharpe ratios of portfolios constructed using linear prediction models. We show that increasing either the number of signals or assets too much makes this procedure susceptible to overfitting and thereby yields wildly overestimated in-sample Sharpe ratios.

We show that low true Sharpe ratio signals are particularly vulnerable to overfitting. Conversely, by extending the length of the in-sample period one can reduce the overfitting risk, and can produce a higher replication ratio out of sample.

We test our results on commodity futures using momentum-style signals and find that allowing AR(1) signals and non-Normal signals/residuals does not significantly impact the validity of our results. In particular, once we match the theoretical out-of-sample Sharpe ratio to the observed value, we see that the replication ratio is primarily a function of the out-of-sample Sharpe ratio and the curves for the AR(1) signals closely matches those of iid signals.

From this analysis, it seems that the best way to minimize the potential for overfitting is to minimize the number of signals and assets that are being used for any predictive model used to trade, and utilize the largest amount of data possible.

In summary, the paper formally demonstrated that to minimize the risk of overfitting, one should,

1. Keep models as simple as possible,
2. Use the longest sensible backtest period available,
3. Develop systems with high Sharpe ratios, and
4. Rely on fewer signals.

While we completely agree with points #1 and #2, our experience casts doubt on points #3 and #4.

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

References

[1] Antoine Jacquier, Johannes Muhle-Karbe, Joseph Mulligan, In-Sample and Out-of-Sample Sharpe Ratios for Linear Predictive Models, 2025, arXiv:2501.03938

Post Source Here: Formal Study of Overfitting in Trading System Design

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Momentum in the Option Market, Part 4-Intraday Case

Momentum in the options market is an emerging and active area of research. For example, Reference [1] demonstrated that delta-hedged straddle positions exhibit momentum, where firms with strong option performance over the past 6 to 36 months are likely to experience high option returns in the subsequent month.

Reference [2] extended this line of research to focus on intraday options returns. The authors pointed out,

In this paper, we uncover novel seasonal patterns in intraday returns on individual stock option straddles. These returns display the same persistent seasonality pattern as those of their underlying stock, even though straddles are delta-neutral. We find straddle return in a given half-hour interval today to positively predicts the return in the same intraday interval tomorrow, especially at the market open and close. These two momentum patterns are driven by different economic forces. While the morning momentum reflects investors’ underreaction to volatility shocks, afternoon momentum is driven by persistent inventory management by option market makers.

In summary, it was shown that a straddle's return during a particular 30-minute trading interval today positively predicts its return during the same interval on subsequent days. Morning momentum reflects a continued under-reaction to overnight volatility news. Afternoon momentum, on the other hand, is attributed to persistent price pressure caused by inventory management from option market makers.

Two important observations were made:

• First, it remains unclear whether the delta-neutral straddles are dynamically rehedged after the trade is initiated throughout the day to maintain neutrality,
• Second, while Reference [1] argued that option momentum is a distinct factor unrelated to stock momentum, the authors of Reference [2] linked morning momentum in options to the underlying stock momentum, suggesting a connection between the two.

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

References

[1] Heston, Steven L. and Jones, Christopher S. and Khorram, Mehdi and Li, Shuaiqi and Mo, Haitao,  Option Momentum (2022). https://ift.tt/yWd8Zxr

[2] Da, Zhi and Goyenko, Ruslan and Zhang, Chengyu, Intraday Option Return: A Tale of Two Momentum (2024). https://ift.tt/nXOb5jk

Post Source Here: Momentum in the Option Market, Part 4-Intraday Case

source https://harbourfronts.com/momentum-option-market-part-4-intraday-case/

Risks of Short-dated Options Order Flow

Options, particularly short-dated ones, are gaining popularity among retail traders, with their trading volume increasing significantly. While some research argues that short-dated options do not impact the market, certain market practitioners hold opposing views.

Reference [1] investigated the risks associated with short-dated options order flow. It examined the effective trading costs of short-dated options, exploring their connection to intraday order flow distribution with the goal of identifying risky patterns that could disrupt a market with high trading volumes. The authors pointed out,

Our analysis documents economically and statistically significant positive relationship between intraday order flow volatility and illiquidity in options market, particularly for ultra-short term options.The effect is pervasive: it holds in the time-series and cross-sectional dimension, and it significantly outweighs the significance of more traditional daily first-moment measures of order flow dynamics, such as volumes or absolute order imbalances. Furthermore, it also outweighs the significance of traditional measures capturing the delta-hedging needs of market makers. These findings suggest that liquidity providers rely primarily on active inventory rebalancing and trade matching throughout the day, with the main source of inventory risk arising from providing liquidity to unbalanced order flows. An exchange-specific analysis further shows that liquidity providers are averse to unpredictable order flows even when they do not directly absorb them, highlighting the role of indirect costs and future liquidity provision risk in the observed relationship.

Our findings underscore the potential risks posed by high volumes in short-term option contracts, which can amplify intraday order flow volatility and challenge market stability. We show that as intraday order flow volatility rises, liquidity providers widen bid-ask spreads to manage the elevated risk, resulting in higher hedging costs for investors increasingly dependent on short-term rollover strategies over long-term hedges. This spread widening, in turn, can impair market efficiency by reducing liquidity and price discovery, which may in turn elevate systemic risk…

In summary, the study finds that,

• Liquidity providers primarily focus on active inventory management and trade matching, using delta-hedging as a secondary risk management strategy.
• Additionally, intraday options order flow has become more volatile since the financial crisis.
• The impact of order flow volatility diminishes with longer maturities, emphasizing the heightened liquidity sensitivity of ultra-short-maturity options.

Ultimately, the study concludes that short-dated options order flow can increase illiquidity, raise trading costs, and destabilize the market.

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

References

[1] Pederzoli, Paola and Doshi, Hitesh and Sert, Saim Ayberk, Risky Intraday Order Flow and Equity Option Liquidity (2024). https://ift.tt/KFvhDTZ

Originally Published Here: Risks of Short-dated Options Order Flow

source https://harbourfronts.com/risks-short-dated-options-order-flow/