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Oct 19

Corpus Prevalence of Multiple-Choice Question Options

In recent years, corpus-driven AI methods, such as Large Language Models (LLMs), have seen widespread use in education. While on the surface their abilities look promising for tasks ranging from generating assessment materials to simulating student performance, we should be aware of the subtle nuances of their frequentist nature that might be affecting their behaviour. In this work, we focus on the aspect of corpus frequency in the context of creating high-quality Multiple Choice Questions (MCQs), specifically asking: What if corpus prevalence were enough to identify the correct answer to an MCQ? We propose a computational method of assessing corpus prevalence of MCQ options in large text corpora leveraging textual embeddings using both expert- and machine-generated MCQ sets. The key finding, across three large question sets, is that correct answers, independently of the question stem, are significantly more available than incorrect options. Specifically, using Wikipedia as the retrieval corpus, we find that always selecting the most prevalent option leads to scores up to 9.0% above the random-guess baseline. We also find that MCQ distractors generated by LLMs often show similar patterns of prevalence compared to expert-created options, despite the LLMs' frequentist nature and their training on large collections of textual data. Moreover, we find that corpus prevalence does not necessarily correlate with how recognisable terms are to humans. This highlights the need to better understand how corpora are used in AI-driven methods for education, whether applied directly or indirectly via LLMs.

  • 3 authors
·
Jun 21

Large Language Models Sensitivity to The Order of Options in Multiple-Choice Questions

Large Language Models (LLMs) have demonstrated remarkable capabilities in various NLP tasks. However, previous works have shown these models are sensitive towards prompt wording, and few-shot demonstrations and their order, posing challenges to fair assessment of these models. As these models become more powerful, it becomes imperative to understand and address these limitations. In this paper, we focus on LLMs robustness on the task of multiple-choice questions -- commonly adopted task to study reasoning and fact-retrieving capability of LLMs. Investigating the sensitivity of LLMs towards the order of options in multiple-choice questions, we demonstrate a considerable performance gap of approximately 13% to 75% in LLMs on different benchmarks, when answer options are reordered, even when using demonstrations in a few-shot setting. Through a detailed analysis, we conjecture that this sensitivity arises when LLMs are uncertain about the prediction between the top-2/3 choices, and specific options placements may favor certain prediction between those top choices depending on the question caused by positional bias. We also identify patterns in top-2 choices that amplify or mitigate the model's bias toward option placement. We found that for amplifying bias, the optimal strategy involves positioning the top two choices as the first and last options. Conversely, to mitigate bias, we recommend placing these choices among the adjacent options. To validate our conjecture, we conduct various experiments and adopt two approaches to calibrate LLMs' predictions, leading to up to 8 percentage points improvement across different models and benchmarks.

  • 2 authors
·
Aug 21, 2023

Application of Deep Reinforcement Learning to At-the-Money S&P 500 Options Hedging

This paper explores the application of deep Q-learning to hedging at-the-money options on the S\&P~500 index. We develop an agent based on the Twin Delayed Deep Deterministic Policy Gradient (TD3) algorithm, trained to simulate hedging decisions without making explicit model assumptions on price dynamics. The agent was trained on historical intraday prices of S\&P~500 call options across years 2004--2024, using a single time series of six predictor variables: option price, underlying asset price, moneyness, time to maturity, realized volatility, and current hedge position. A walk-forward procedure was applied for training, which led to nearly 17~years of out-of-sample evaluation. The performance of the deep reinforcement learning (DRL) agent is benchmarked against the Black--Scholes delta-hedging strategy over the same period. We assess both approaches using metrics such as annualized return, volatility, information ratio, and Sharpe ratio. To test the models' adaptability, we performed simulations across varying market conditions and added constraints such as transaction costs and risk-awareness penalties. Our results show that the DRL agent can outperform traditional hedging methods, particularly in volatile or high-cost environments, highlighting its robustness and flexibility in practical trading contexts. While the agent consistently outperforms delta-hedging, its performance deteriorates when the risk-awareness parameter is higher. We also observed that the longer the time interval used for volatility estimation, the more stable the results.

  • 3 authors
·
Oct 9, 2025