Do Rough Volatility Models Improve Option Pricing?

The Black-Scholes-Merton (BSM) model is the cornerstone of derivatives pricing. However, because of its limitations, several extensions have been developed since its introduction. Reference [1] explores another direction for extending option pricing models by incorporating the roughness of volatility.

Specifically, the authors implement the rough Bergomi and rough Heston models and compare their performance with standard stochastic volatility models, including one with jumps. The study uses KOSPI 200 options data from January 2003 through June 2025, covering 5,571 trading days. Only at-the-money (ATM) and out-of-the-money (OTM) options with maturities of up to 180 days are included. The models are then evaluated both in-sample and out-of-sample.

The author pointed out,

This study compares the pricing performance of the rough volatility models (rBergomi and rHeston) and the classical models (SV; SVJDE ; SVJLN) in the KOSPI 200 index options market, applying the deep surrogate methodology in daily calibration and out-of-sample forecasting experiments over the 22 years from 2003 to 2025. In-sample, the nine-parameter SVJDE model performed best, but the difference from the rBergomi model, which uses only three core parameters, was not large. Out of sample, by contrast, rBergomi performed best at every forecast horizon. We attribute this to a structural limitation of the SVJ models, whose jump parameters overfit the current-day surface and cannot adapt to market conditions that change abruptly in a crisis. rBergomi, in contrast, maintained stable performance even in extreme environments, owing to its parsimony and to the structural flexibility of being able to reestimate the entire forward variance curve.

In short, the paper finds that KOSPI 200 volatility is empirically rough and that the rough Bergomi model delivers the best out-of-sample pricing performance.

It is worth noting that although the rough Bergomi model appears to have fewer parameters (three), its reliance on the forward volatility curve as an input effectively increases the number of parameters required.

While the study demonstrates the usefulness and strong pricing performance of rough volatility models, their effectiveness in hedging and trading remains to be evaluated.

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

References

[1] Jang, W. W. (2026). Empirical performance of rough volatility models in the KOSPI 200 options market using deep surrogates, Journal of Derivatives and Quantitative Studies.

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Why Has Trend-Following Profitability Declined?

Trend following is an investment strategy that seeks to profit from sustained price movements across financial markets. It has long been a popular strategy. However, there are signs that its profitability has declined. In a previous post, we discussed the decline of Trend-Following CTAs.

In a similar context, Reference [1] examines why futures trend-following performance has deteriorated since 2008 and explores ways to improve its profitability. The author analyzes 75 futures markets across six asset classes from January 1990 to August 2026, using data from Norgate Data. The study employs a time-series momentum strategy that takes positions based on the sign of the preceding 12-month return and holds them for one month. Positions are volatility-scaled, with equal risk allocation across markets.

The paper pointed out,

The evidence forms a coherent chain. The 12-month continuation opportunity weakened, and the monthly Moskowitz 12/1 benchmark remains profitable after exact delivery-level costs but produces only a 0.42 post-2008 net Sharpe. A 252-day slope offers a complementary trend definition, although its stand-alone advantage is not decisive. The horizon experiment then shows that decay is concentrated in rules that replace the complete signal vintage every month. Combining all 12 lookback and holding-period rules in one equal-weight, internally netted book raises net Sharpe to 0.62 and reduces maximum drawdown to 12.8% without choosing the best cell after observing the data. Correlation-aware weighting does not improve that simple portfolio.

The funded analysis changes the scale of the question but not its economic meaning. After the common liquidity screen, the multi-horizon book produces a 0.64 Sharpe above cash and a 9.1% maximum drawdown; the sign-slope ensemble produces the highest funded CAGR at 6.74%. Both have statistically positive Sharpe advantages over the capped benchmark. Most transaction participation is low, but isolated events between 29% and 38% remain outside what daily data can validate as one-session execution. The recommendation is therefore a portfolio design plus an execution constraint, not an unrestricted capacity claim.

In short, the study concludes that trend following remains profitable, but its profitability has declined due to weaker underlying trend continuation, particularly in equity-index and currency futures. Interest-rate and agricultural futures, however, have shown greater resilience. The paper also finds that correlation-based optimization does not materially improve risk-adjusted returns, whereas diversification across multiple trend horizons does.

An important takeaway is the value of diversification, not only across asset classes but also across trading time frames and trend horizons.

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

References

[1] Bang, P. (2026). Trend Following in Modern Futures Markets: Separating Opportunity Decay, Signal Conversion, and Implementation. Working paper.

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Pricing Derivatives with Mean-Reverting Stochastic Strikes

Financial derivatives are an integral part of modern financial markets, serving important roles in risk management, hedging, and speculation. Since the development of the Black-Scholes-Merton (BSM) model for pricing plain vanilla options, increasingly exotic options have emerged, and quantitative analysts have developed pricing formulas for these instruments.

In this context, Reference [1] develops a closed-form pricing formula for a financial contract whose payoff depends on the difference between two stochastic variables rather than a conventional fixed strike. In other words, the fixed strike in a vanilla option's payoff is replaced by a mean-reverting stochastic variable.

The authors argue that the benchmark's mean-reverting dynamics prevent it from being treated as a directly traded asset under their model, making the market incomplete. Consequently, the benchmark's market price of risk must be specified or calibrated, rather than determined solely by no-arbitrage. They pointed out,

This paper has developed an analytically tractable valuation framework for contracts whose payoff depends on the difference between an underlying asset and a non-tradable, mean-reverting benchmark, with applications to the integrated management of financial, operational, and emerging risks. The paper makes several key theoretical contributions.

First, it provides a formal proof that mean-reversion precludes tradability of the benchmark, requiring the specification of a market price of risk. Second, it derives closed-form pricing formulae for contracts that are linked to the Black–Scholes–Merton structure through a risk-neutral expected benchmark and an expanded effective variance. Importantly, these contracts should not be interpreted as standard vanilla options with fixed contractual strikes; the fixed-strike Black–Scholes–Merton case is recovered only when benchmark uncertainty vanishes, or the benchmark becomes effectively deterministic. Third, it provides a systematic analysis of how cost volatility, mean-reversion speed, and cross-process correlation jointly determine investment option value in a real options setting. Fourth, it applies the formulation to three economically important classes of derivatives: weather derivatives, volatility index options, and inflation-linked instruments.

In short, the paper develops a closed-form pricing formula for a financial contract whose payoff contains a strike that is not fixed but is instead a mean-reverting stochastic variable.

This is an interesting contribution to derivatives pricing. As the authors point out, the formula can be applied to real options, volatility, inflation, and weather derivatives.

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

References

[1] Carvalho, P. V., Pinheiro, C. M., & Reis, J. M. (2026). Pricing contracts on a tradable asset and a non-tradable mean-reverting benchmark: Closed-form formulae and applications. Cogent Economics & Finance, 14(1), 2740368.

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How AI and Passive Investing Affect Stock Market Behavior

Artificial Intelligence (AI) is increasingly in the spotlight, attracting widespread attention across industries. One question on investors’ minds is how AI will change investment dynamics. In this context, Reference [1] examines whether AI and passive investing weaken the relationship between stock returns and economic fundamentals while increasing return autocorrelation.

The study analyzes 12 Fama-French U.S. industry portfolios using quarterly data from 2002 Q1 to 2025 Q2, comprising 1,128 industry-quarter observations. To measure AI sentiment, the author uses NVIDIA’s excess returns over the S&P 500, detrended and standardized.

The paper pointed out,

Five findings stand out. First, AI intensity exerts a robust negative effect on quarterly industry returns, acting as a sectoral redistributive force that diverts capital from non-AI segments during sentiment spikes – consistent with Danielsson and Uthemann’s (2025) prediction of intensified procyclical, synchronised capital behaviour – without directly severing the informational relationship between prices and economic activity. Second, fundamental anchoring persists over the full 2002–2025 period but is weakening. Industrial production growth retains its role as a positive and significant predictor of industry returns, although rolling-window and split-sample analyses reveal a sustained deterioration from 2015 Q2 that intensifies in the post-COVID era. Third, no evidence of feedback dynamics emerges: the lagged-return coefficient fails to attain statistical significance throughout the sample and across both sub-periods, providing no support for the market-fragility hypothesis and aligning instead with informationally efficient pricing. Fourth, passive investing flows exert no direct effect on returns, suggesting their influence operates through indirect structural channels–factor exposure, amplified comovement, and liquidity transformation– in line with the microstructure mechanisms identified by Ben-David et al. (2018) and Da and Shive (2018). Fifth, aggregate market returns remain the dominant driver of industry variation, a pattern that neither AI sentiment nor passive growth has yet materially altered.

In short, the paper finds that when AI-related stocks perform particularly well, other industries tend to underperform. This suggests that investors may be shifting capital toward AI companies and away from traditional sectors. The study also finds that stock returns have become less closely linked to economic fundamentals since 2015, although the evidence of this weakening is relatively modest.

This paper contributes to an emerging body of research on the impact of AI on investing, although its real-world effects remain to be seen.

An interesting aspect of the study is its use of NVIDIA’s relative performance as a proxy for AI sentiment. Trading system developers could adopt a similar approach by incorporating similar AI-related variables into investment models.

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

References

[1] Piscopiello, M. (2026). Artificial Intelligence, Price Anchoring, and Feedback Dynamics in U.S. Equity Markets, Kent Economics Undergraduate Research Journal, Issue 4.

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The Relationship Between Leverage, Investor Behavior, and Returns

Margin lending and borrowing are integral parts of a well-functioning financial system. However, excessive use of margin, or leverage, can create significant risks. In this context, Reference [1] examines the returns and trading behavior of retail investors using margin financing in the Chinese stock market.

The study uses transaction data from nearly five million brokerage accounts between May and July 2015, covering China's equity market bubble and crash. The authors report an average assets-to-equity ratio of 1.4 for brokerage margin accounts and 6.4 for shadow accounts. They then construct a distance-to-margin-call measure (Z), which estimates how many standard deviations of portfolio losses would bring an account to its liquidation threshold.

The paper  pointed out,

We find that margin traders tend to hold stocks with more scope for “informed trading” and lottery-like features, though they do not outperform their unlevered counterparts. Our results thus suggest that lottery preferences, partly driven by overconfidence, can help explain why investors are willing to pay an annual interest rate of up to 25% in order to lever up.

Both shadow and brokerage margin investors heavily sell their holdings when their account-level leverage edges toward their Pingcang Lines (the maximum leverage limit, or maintenance margin), controlling for stock-date and account fixed effects. In other words, we find strong empirical support for both forced and preemptive margin-induced trading. The fact that investors react asymmetrically to positive and negative return shocks suggests a leverage constraint channel in addition to a rebalancing motive. We exploit the discontinuity around the eligibility of brokerage margin trading and the variation in Pingcang Lines across certain shadow accounts to provide unique evidence that leverage constraints induce selling. Moreover, we find that margin investors are relatively more likely to sell non-lottery stocks as the leverage constraint binds in a down market.

Aggregating trading behavior across margin investors, we find a significant return spillover in the near future: a stock’s return can be strongly forecasted by a portfolio of stocks with which it shares common margin-investor ownership. This pattern is subsequently reversed, and is present only in market downturns.

In short, the paper finds that,

• Retail margin borrowing is associated with lottery preferences and possible overconfidence.
• Margin-induced liquidation creates a feedback loop between declining asset prices and forced selling, transmitting shocks across otherwise unrelated stocks.

Although the study focuses on leveraged trading in the Chinese stock market, its conclusions may also be applicable to developed markets. We would be interested to hear from readers who are aware of similar studies in developed markets.

Another interesting contribution is the adaptation of the Merton credit risk model to leveraged trading, providing a framework for analyzing margin-related risks.

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

References

[1]  Jiangze Bian, Zhi Da, Zhiguo He, Dong Lou, Kelly Shue, and Hao Zhou, The Drivers and Implications of Retail Margin Trading, Journal of Finance, 2026.

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Revisiting Gambler’s Ruin: Trading Edge, Drawdowns, and Survival

The gambler's ruin problem is a classical probability problem that examines the likelihood of a gambler reaching a specified wealth target or losing all available capital. Reference [1] revisits this problem. Specifically, it seeks to answer the following questions:

Suppose a gambler enters a casino with finite capital,

• What is the probability of reaching a target wealth level or going bankrupt, and
• What is the expected duration of play?

The author first derives analytical formulas to address these questions, then uses Monte Carlo simulations to validate the theoretical results. Finally, the findings are applied to a real-world investment problem using daily S&P 500 data from January 1990 through September 2026.

The author pointed out,

Applied to daily S&P 500 returns, the model estimates a win rate of p = 0.5369 and finds that the sign sequence is statistically distinguishable from an independent one while being, in magnitude, very nearly independent. The more serious failure is elsewhere. When the fixed unit stake is replaced by a bootstrap of the actual return distribution, holding the win rate and the mean absolute move constant, the projected probability of ruin rises from 5.0% to 42.7%. The model’s weakness is not that markets are predictable but that they do not move in equal steps. That is a useful thing to know about a model, and it is the kind of thing that only becomes visible when the mathematics is exact enough that the discrepancy cannot be blamed on the algebra.

A central finding of the paper is that risk models based solely on the frequency of winning/losing days can substantially underestimate the risk of ruin when actual return magnitudes are unequal and heavy-tailed. In other words, the size of losses relative to gains, as well as the presence of fat tails, is critical in determining ruin probabilities.

Another interesting finding is that a relatively small increase in the probability of winning can dramatically reduce the probability of ruin. For example, at a 51% win rate, the probability of ruin is 44.93%, whereas at a 56% win rate, it falls to just 0.8%.

This paper makes an important contribution by formally confirming two principles already familiar to practitioners, namely

• Keeping losses and drawdowns small, and
• Increasing the trading edge whenever possible.

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

References

[1] Jasman Mander, Random Walks and the Gambler’s Ruin Problem: Exact Results, Independent Derivations, and an Empirical Application to Equity Index Returns, Working Paper, 2026

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Market Timing Strategies Using the Implied Volatility Surface

Market timing is typically conducted using technical, macroeconomic, and volatility indicators. However, there is a growing trend in the research community toward using options-implied volatility to extract information for constructing market-timing strategies. For example, we have discussed how option-implied distributions can be used to time the market. Along the same line, Reference [1] develops an approach that uses the implied-volatility surface (IVS) to identify market entry points.

Using the IVS, the authors develop two groups of indicators,

1. Directional-expectation indicators: Directional Sentiment Bias (DSB) and Relative Upside Conviction (RUC).
2. Risk-stability indicators: Tail Risk Concentration (TRC) and Intertemporal Uncertainty Spread (IUS).

These indicators are then combined into three bullish structural regimes:

1. Extreme Hedging Reversal: panic/hedging conditions remain elevated, but directional sentiment has already turned bullish.
2. Trend-Stabilizing Correction: short-term stress has subsided relative to longer-term uncertainty while bullish sentiment remains.
3. Persistent Trend Potential: low short-term stress and longer-term uncertainty combined with bullish conviction, interpreted as conditions favorable to continued trends.

The authors test their approach on AAPL, TSLA, NVDA, and SPY. They generate an entry signal when IVS structural indicators cross dynamically calibrated thresholds into a defined regime, using only the first day of each structural transition as the entry point.

The paper pointed out,

The timely identification of effective market entry points is critical for capturing favorable risk-return opportunities while mitigating downside exposure. To address this challenge, the proposed framework leverages the structural information contained in the IVS through an economically motivated segmentation into the Central Sentiment and Peripheral Risk domains. Structural factors extracted from these domains disentangle directional sentiment from extreme risk pricing, while regime-specific thresholds identify distinct structural market regimes. By focusing on IVS state transitions rather than continuous price movements, this approach identifies discrete, effective entry points. Experimental results show that the framework outperforms conventional price-based and volatility-level baselines in directional accuracy and risk-adjusted returns. These findings highlight the practical value of structurally informed IVS analysis for precise, early-phase entry point detection and tactical decision-making in financial markets.

In short, the authors find that the IVS strategy generally delivers higher risk-adjusted performance, although the magnitude varies materially across assets. Their interpretation is that combining directional information with structural risk conditions improves entry timing.

A noteworthy conclusion is that this approach produced more precise and robust early-phase entry points than the technical and sentiment benchmarks tested, particularly because it uses economically interpretable information from different regions of the IV surface rather than continuously forecasting prices. Consequently, the approach can be used as a standalone regime-detection framework.

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

References

[1] Yi-Chieh Sung, Shiou-Chi Li, and Jen-Wei Huang, Market Timing via Structural Transition Detection in the Options Implied Volatility Surface, in Advances in Computational Collective Intelligence, Springer 2026

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Statistical Arbitrage in Prediction Markets

Prediction markets are markets in which participants trade contracts based on the outcomes of future events, and they have become increasingly popular in recent years. Given their rising popularity, an important question is how to develop quantitative betting strategies.

Reference [1] proposes an interesting approach based on an adaptation of the classic pairs-trading strategy. Specifically, the paper adapts financial-market pairs trading and mean reversion to U.S. presidential betting markets. But instead of modeling the price spread between two stocks, it models the sum of the implied probabilities of the presidential nominees.

The combined probability is modelled as a latent Ornstein-Uhlenbeck (OU) process with a time-varying mean plus additive observation noise. The OU component represents short-term mean reversion, while the moving equilibrium represents gradual changes in the election market.

The authors utilize political betting odds obtained through BetData. The 2020 election (Trump/Biden) is used for model construction and training, while the 2024 election (Trump/Harris) is used for out-of-sample testing. They pointed out,

This study demonstrates the feasibility of adapting a pairs-trading framework to political prediction markets. We model the combined implied probability of the two major-party nominees using a latent time-varying-mean Ornstein-Uhlenbeck process with additive observation noise, use bootstrap-based prediction bounds to identify trading signals, and apply a Bradley-Terry pairwise comparison model to select the candidate-specific odds. In the 2024 out-of-sample evaluation, the strategy generated 130 completed trades, with a mean realized odds-price return of 1.86% and an unannualized per-trade Sharpe-type ratio of 1.12. These results illustrate the potential of the integrated signal-generation and candidate-selection framework in electoral markets dominated by two leading candidates.

In short, the authors present the framework as a proof of concept showing that a pairs-trading-style mean-reversion model can be adapted to two-candidate political betting markets. They point to the 2024 130-trade out-of-sample result, +1.86% mean synthetic odds-price return and 1.12 per-trade Sharpe-type ratio as evidence for the integrated signal-generation/candidate-selection framework.

This is an interesting paper, as it provides a foundation for developing quantitative strategies in prediction markets.

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

References

[1] Haoyu Liu, Len Thomas, Benjamin Baer, and Carl Donovan, Adapting Pairs Trading to Gambling Markets: A Case Study of the U.S. Presidential Election, arXiv 2609.22639v1, 2026

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Understanding P&L in Risk Reversal Strategies

Option P&L attribution is an important component of portfolio and risk management. We have previously discussed related topics, including how option P&L is path-dependent. Reference [1] examines P&L attribution and, specifically, the sources of P&L in a risk-reversal position, a structure commonly used to express a view on volatility skew.

The author investigates the problem both within a formal framework and empirically, using 886 SPY risk reversal trades from 2020–2026, marked daily. An equal-delta risk reversal consists of a long position in one OTM wing and a short position in the other at equal absolute deltas, with the overall position delta-hedged.

The author pointed out,

…The frame is natural: the risk reversal is the canonical vanna-bearing structure, and vanna is how the vanna–volga pricing tradition prices the smile’s slope. This paper argues the frame inverts the economics of the delta-matched, hedged version of the trade. Deriving the structure’s Greeks from first principles and reconciling a five-year, 886-trade tape’s P&L into Greek buckets—exactly, so the decomposition is confirmed rather than fitted—we find that the money is made by differential vega applied to skew mean-reversion, that the vanna term is a structural cost whose sign is pinned by the leverage effect, and that the two facts are connected by an impossibility result: the vanna cannot be removed with the structure’s own legs, at any positive weighting.

In short, the paper finds that the P&L comes from differential vega applied to skew mean reversion, while vanna is a structural cost. Furthermore, vanna cannot be eliminated using just the two option legs.

This is an interesting paper that [glossary_exclude]warrants [/glossary_exclude]further investigation. Several questions remain worth exploring. For example,

• Can other structures be used in which vanna is not a cost?
• And what happens when the spot-volatility correlation changes sign, as it has done recently?

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

References

[1] Charlie Yan, A Formal Theory of the Delta-Matched Risk Reversal: Slope Vega, Irreducible Vanna, and a Dollar-Reconciling Attribution, Working paper 2026.

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Credit Spreads as Predictors of Equity Market Returns

Credit risk is the risk of financial loss arising from a borrower’s failure to meet its debt obligations. However, credit risk not only affects credit markets but can also affect equity markets, for example, through options volatility and returns. We have previously discussed how credit risk affects the returns of momentum strategies.

Along the same line, Reference [1] examines whether movements in corporate credit spreads reliably predict future U.S. equity-market performance. The hypothesis is that widening IG/HY spreads precede lower S&P 500 returns, narrowing spreads precede higher returns, and predictive strength varies across market regimes.

The author uses monthly data from January 2000 to July 2025, comprising approximately 305 observations. The dataset includes ICE BofA investment-grade (IG) and high-yield (HY) option-adjusted spreads (OAS), 10-year Treasury and 3-month T-bill yields, and the S&P 500 Total Return Index. The analysis employs OLS regressions with Newey-West HAC standard errors, with additional specifications controlling for the Treasury term spread and lagged equity returns.

The paper pointed out,

The results indicate that corporate credit spreads, especially changes in Investment-Grade (IG) spreads, carry meaningful predictive information about equity market performance. The consistently negative regression coefficients show that widening spreads are typically followed by weaker S&P 500 returns, supporting the hypothesis that tightening credit conditions signal rising risk aversion and slower economic growth. This relationship was strongest during 2008-2015, when financial stress was elevated, suggesting that the predictive power of spreads depends on market conditions and becomes more useful in periods of heightened uncertainty. The later 2016–2025 period shows a different pattern, with some predictors displaying positive coefficients. This reflects the unusual macroeconomic environment following the COVID-19 shock, where aggressive monetary intervention and rapid market recoveries caused spreads to widen during rebounds rather than deteriorations. This suggests that the credit-equity link is not constant, but shifts depending on the dominant macro regime.

These findings reinforce the idea that credit markets often reprice risk before equities. Credit spreads reflect how investors view the overall level of risk in the market, including the chances of default, the availability of liquidity, and expectations about the broader economy. When they widen, it reflects a deterioration in market confidence that later translates into weaker corporate earnings and stock performance. This result supports earlier studies suggesting that movements in credit spreads can signal where the economy and financial markets are headed, reflecting shifts in overall risk.

In short, the results indicate that corporate credit spreads, particularly changes in investment-grade spreads, contain predictive information about equity returns. Widening spreads generally precede weaker S&P 500 returns, although the relationship varies across market regimes and was strongest during 2008–2015. The findings suggest that credit markets can reprice risk before equities, making credit spreads potentially useful indicators of subsequent equity-market performance.

These findings provide further evidence that developments in credit markets can affect equity markets. The results can be used directly as trading signals, or the variables can be incorporated into a regime-detection algorithm.

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

References

[1] Vishwa Kalal, Corporate Credit Spreads as Predictors of Equity Market Performance, AlgoGators Capstone Project, 2025.

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