Wednesday, July 23, 2025

Can AI Trade? Modeling Investors with Large Language Models

Large language models (LLMs) are advanced artificial intelligence systems trained on vast amounts of text data to understand and generate human-like language. LLMs can perform a wide range of language tasks, including translation, summarization, question answering, and code generation. Their versatility has made them valuable tools across industries, from finance and healthcare to education and software development.

Reference [1] utilized LLMs to construct trading agents in the financial markets. Specifically, the author used LLMs to emulate various types of investors: value investors, momentum traders, market makers, retail traders, etc. The article pointed out,

First, LLMs can effectively execute trading strategies. They consistently understand market mechanics, process market information, form price expectations, and execute trades according to specific instructions. Their trading behavior is highly sensitive to the prompts they receive—they faithfully follow directions regardless of profit implications…

Second, LLMs react meaningfully to market dynamics. They consider current and historical prices, dividends, and other market information when making decisions. …

Third, market dynamics with LLM agents can resemble actual markets and mirror classic results from the theoretical finance literature. When these agents interact, they produce realistic price discovery and liquidity provision with emergent behaviors, including price convergence toward fundamental values…

These findings carry significant implications for market structure and regulation. While LLM agents can enhance price discovery and liquidity, their adherence to programmed strategies, even potentially flawed ones derived from prompts, could amplify market volatility or introduce novel systemic risks, as observed in our simulated bubble scenarios. A key concern is the potential for widespread correlated behavior: similar underlying LLM architectures responding uniformly to comparable prompts or market signals could inadvertently create destabilizing trading patterns without explicit coordination. This underscores the critical need for rigorous testing and validation of LLM-based trading systems prior to live deployment.

In short, the article concluded that trading strategies generated by large language models are effective, but could introduce new systemic risks to financial markets because these agents would act in a correlated manner.

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

References

[1] Alejandro Lopez-Lira, Can Large Language Models Trade? Testing Financial Theories with LLM Agents in Market Simulations, arXiv:2504.10789

Article Source Here: Can AI Trade? Modeling Investors with Large Language Models



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Friday, July 18, 2025

Improving Hedging with Skew-Adjusted Delta

Delta hedging is a method used to reduce or eliminate the directional risk of an options position. In most delta hedging schemes, delta is calculated using the Black-Scholes-Merton (BSM) model. However, the BSM delta is not always accurate due to the assumptions embedded in the model. For a more accurate hedge, adjustments need to be made. We have discussed such an adjustment proposed by Hull and White.

Following this line of research, Reference [1] examined the use of skew-adjusted delta for hedging. The paper retested the method developed by Vähämaa [2] and applied it to S&P 500 index options during the COVID-19 pandemic. Specifically, the author modified the BSM delta as follows,

The author pointed out,

Considering the second hypothesis (H2), the performance of the smile-adjusted delta was retested with data from the S&P 500 index. Both models’ quantitative fit is documented to be approximately 90%, but SAD explains daily option price movements slightly better than the BS delta, regardless of the moneyness and maturity of the option. Indicating, it is reliable to finally compare the delta hedging performance of the two deltas.

The overall conclusion is that SAD outperforms the BS delta in delta hedging, meaning that the second hypothesis (H2) is also true. To contradict Vähämaa’s (2004) results, the empirical finding from delta hedging indicates that SAD outperforms the BS delta most distinctly among ITM options. When the hedging horizon is longer than a day, SAD outperforms the BS delta regardless of the moneyness and maturity of the option. That out-performance becomes even more notable as the hedging horizon lengthens. This out-performance increase is even more distinct than what Vähämaa (2004) documented. This may be due to the relatively steep volatility smile making the smile-adjustment term, or specifically considering the slope of the smile, more crucial.

In short, the article shows that skew-adjusted delta (SAD) performs better than BSM delta, especially for in-the-money options. When the hedge lasts more than one day, SAD outperforms BSM delta across all moneyness and maturities, with the advantage growing as the hedging period gets longer.

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

References

[1] Berg, Wille, From the inaccurate Black-Scholes model to more efficient delta hedging with smile-adjusted extension,  University of VAASA, 2025

[2] Vähämaa, S., Delta hedging with the smile, Financial Markets and Portfolio Management, 18(3), 241-255, 2004

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Saturday, July 12, 2025

Bitcoin Trend Following Strategies vs. Traditional Indices: A Comparative Study

Trend following is an investment strategy that seeks to capture gains by identifying and trading in the direction of established market trends. Trend followers aim to ride sustained movements, upward or downward, using rules-based systems often driven by price momentum, moving averages, or breakout signals.

Trend following is a popular investment strategy among both individual and institutional investors. Reference [1] examined and compared the performance of the trend following strategy in the U.S., China, and cryptocurrency markets.

The paper applies trend-following strategies using simple, exponential, and double exponential moving averages. For BTCUSD, the S&P 500, and the CSI 300 Index, short windows of 1–20 days and long windows of 21–50 days are used. A buy signal is triggered when the short-term average exceeds the long-term average, and a sell signal when it falls below.

The authors pointed out,

The results of this paper show that: first, the Bitcoin trend-following strategy performs more significantly than the traditional financial index under special market conditions (such as during the COVID-19 epidemic); second, the DEMA trend-following strategy of Bitcoin is relatively stable in terms of Sharpe ratio, especially in the bear market; Third, there is a trend of negative or no correlation between Bitcoin and traditional financial indexes, indicating that Bitcoin may serve as an effective hedging tool.

In short, the study finds that Bitcoin trend-following strategies outperform traditional indices during market stress, show stable Sharpe ratios in bear markets, and exhibit low or negative correlation with traditional assets, suggesting Bitcoin's potential as a hedge.

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

References

[1] L Mo, L Wang, Z Zhang, K Huang, Effectiveness Test of Trend Following Strategy for Emerging Assets and Traditional Assets: A Case Study of Digital Currency and Index Futures, Modern Management based on Big Data VI, 2025

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Wednesday, July 9, 2025

Reducing Path Dependency in Options PnL

The profit and loss of an options trading strategy can be path-dependent, meaning that interim price movements, not just the final outcome, significantly influence profits and losses due to factors like dynamic hedging, early exercise risk, and volatility shifts.

A well-known example is the PnL of a delta-hedged option position, where the outcome depends on the path. Even if we estimate the realized volatility correctly, we still cannot determine the exact profit or loss, because the PnL is path-dependent.

How can we reduce this path dependency?

Reference [1] proposed the use of a laddering technique. The authors pointed out,

Laddering is a practical and effective solution to mitigate the risks of path dependency in option income strategies. Unlike single-path strategies that rely on fixed expirations and trade dates, laddering involves staggering option expirations and strike levels across different time frames. This approach reduces reliance on specific market outcomes, creating a smoother income stream and a more resilient portfolio structure.

Exhibit 28.2 highlights the significant benefits of laddering by combining one-month period for each trading day of the month. The results demonstrate that laddered strategies reduce return variability compared to single-path strategies, which depend heavily on specific market conditions at expiration. By diversifying expirations and strikes, laddering ensures a steady flow of income while minimizing the impact of adverse market events. The laddering approach may also improve liquidity, enabling portfolio managers to incrementally adjust their portfolios more effectively in response to market changes. This makes laddering an indispensable tool for managing path dependency and achieving consistent portfolio performance.

In short, the author advocates the commonly used approach of diversification, specifically, diversifying entry times and strike selections.

This approach is reasonable and widely accepted. However, we note that what the author refers to here is more accurately a mitigation of the negative outcomes resulting from “unlucky” paths. In a covered call strategy, since no dynamic hedging is performed, the final PnL depends on the terminal distribution of the underlying only. Nevertheless, the same technique applies equally to strategies that involve dynamic hedging.

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

References

[1] John Burrello, Managing Path Dependency and Balancing Yield in Option Income Strategies, In: Fabozzi, F.J., de Jong, M. (eds) Derivatives Applications in Asset Management. Palgrave Macmillan, Cham.

Originally Published Here: Reducing Path Dependency in Options PnL



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Friday, July 4, 2025

Harvesting the Equity Risk Premia Through Options

The equity risk premium refers to the excess return that investing in the stock market provides over a risk-free rate, typically represented by government bonds. It compensates investors for taking on the higher risk associated with equities. Estimating the equity risk premium is essential for asset allocation, valuation models, and long-term return expectations in portfolio management.

Reference [1] investigates the use of stock options to capitalize on the equity risk premium. It studied all the U.S. optionable stocks. The study first utilized a machine learning method to estimate expected stock returns (ESR). Then, each month, it sorted at-the-money call options by the ESR of the underlying stock and constructed a long-short portfolio: buying calls on high-ESR stocks and selling calls on low-ESR stocks, holding these positions to maturity. The authors pointed out,

We study via a simple test whether options are a useful tool to harvest the risk premia of the underlying stocks. We introduce a trading strategy that buys calls on stocks with high expected stock returns, and sells calls on stocks with low expected stock returns, and vice versa for puts. We find that these two trading strategies deliver surprisingly low returns, which do not even outperform a naive investment that simply buys all available call or put options, i.e., the “market”…

This finding has two important implications. First, it shows that options are not a useful tool to extract stock risk premia. Second, it implies that option prices are not independent of the underlying’s expected return—violating a central insight of option pricing theory. To corroborate our findings, we apply machine learning techniques to predict expected option returns and option prices. We find that variables predicting stock returns well, do barely predict option returns, but explain option prices well. Moreover, if we use our direct estimate of the expected stock return as a predictor variable, we again find that it predicts price levels well, but not returns.

Finally, we find violations of put-call-parity consistent with our result. In particular, the level of expected stock return is a strong predictor of the implied volatility spread between a pair of calls and puts. This suggest that options are priced such that they largely offset the effects of the underlying’s expected return on the expected option returns.

In short, the article concluded that,

  • Options are not effective instruments for capturing stock risk premia,
  • Option prices are influenced by the expected returns of the underlying stocks, which challenges a core assumption of traditional option pricing theory.

These findings are interesting and somewhat surprising. However, we note that they apply only to cross-sectional returns. As observed by the authors, if one has a directional bias, then simply buying calls can deliver respectable risk-adjusted returns. Hence, in the time-series momentum space, having a directional edge could be augmented by using options.

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

References

[1] d'Avernas, Adrien and Schlag, Christian and Sichert, Tobias and Sichert, Tobias and Waibel, Martin and Wang, Chunjie, Betting on Stocks with Options?, Swedish House of Finance Research Paper No. 2025-03 https://ift.tt/Ap1GTJQ

Originally Published Here: Harvesting the Equity Risk Premia Through Options



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