Quantitative Finance

Jaber, Eduardo Abi

doi: 10.48550/arxiv.2412.11264pmid: N/A

Abstract:We introduce a simple, efficient and accurate nonnegative preserving numerical scheme for simulating the square-root process. The novel idea is to simulate the integrated square-root process first instead of the square-root process itself. Numerical experiments on realistic parameter sets, applied for the integrated process and the Heston model, display high precision with a very low number of time steps. As a bonus, our scheme yields the exact limiting Inverse Gaussian distributions of the integrated square-root process with only one single time-step in two scenarios: (i) for high mean-reversion and volatility-of-volatility regimes, regardless of maturity; and (ii) for long maturities, independent of the other parameters.

Long, Wo; Xiao, Victor

doi: 10.48550/arxiv.2412.11432pmid: N/A

Abstract:The residuals in factor models prevalent in asset pricing presents opportunities to exploit the mis-pricing from unexplained cross-sectional variation for arbitrage. We performed a replication of the methodology of Guijarro-Ordonez et al. (2019) (G-P-Z) on Deep Learning Statistical Arbitrage (DLSA), originally applied to U.S. equity data from 1998 to 2016, using a more recent out-of-sample period from 2016 to 2024. Adhering strictly to point-in-time (PIT) principles and ensuring no information leakage, we follow the same data pre-processing, factor modeling, and deep learning architectures (CNNs and Transformers) as outlined by G-P-Z. Our replication yields unusually strong performance metrics in certain tests, with out-of-sample Sharpe ratios occasionally exceeding 10. While such results are intriguing, they may indicate model overfitting, highly specific market conditions, or insufficient accounting for transaction costs and market impact. Further examination and robustness checks are needed to align these findings with the more modest improvements reported in the original study. (This work was conducted as the final project for IEOR 4576: Data-Driven Methods in Finance at Columbia University.)

van Staden, Pieter; Forsyth, Peter; Li, Yuying

doi: 10.48550/arxiv.2412.05431pmid: N/A

Abstract:Leveraged Exchange Traded Funds (LETFs), while extremely controversial in the literature, remain stubbornly popular with both institutional and retail investors in practice. While the criticisms of LETFs are certainly valid, we argue that their potential has been underestimated in the literature due to the use of very simple investment strategies involving LETFs. In this paper, we systematically investigate the potential of including a broad stock market index LETF in long-term, dynamically-optimal investment strategies designed to maximize the outperformance over standard investment benchmarks in the sense of the information ratio (IR). Our results exploit the observation that positions in a LETF deliver call-like payoffs, so that the addition of a LETF to a portfolio can be a convenient way to add inexpensive leverage while providing downside protection. Under stylized assumptions, we present and analyze closed-form IR-optimal investment strategies using either a LETF or standard/vanilla ETF (VETF) on the same equity index, which provides the necessary intuition for the potential and benefits of LETFs. In more realistic settings, we use a neural network-based approach to determine the IR-optimal strategies, trained on bootstrapped historical data. We find that IR-optimal strategies with a broad stock market LETF are not only more likely to outperform the benchmark than IR-optimal strategies derived using the corresponding VETF, but are able to achieve partial stochastic dominance over the benchmark and VETF-based strategies in terms of terminal wealth.

Liang, Zongxia; Wang, Sheng; Xia, Jianming

doi: 10.48550/arxiv.2412.02446pmid: N/A

Abstract:This paper discusses a nonlinear integral equation arising from portfolio selection with a class of time-inconsistent preferences. We propose a unified framework requiring minimal assumptions, such as right-continuity of market coefficients and square-integrability of the market price of risk. Our main contribution is proving the existence and uniqueness of the square-integrable solution for the integral equation under mild conditions. Illustrative applications include the mean-variance portfolio selection and the utility maximization with random risk aversion.

Garnier-Brun, Jerome; Zakine, Ruben; Benzaquen, Michael

doi: 10.1103/3bj7-jc92pmid: 40981592

Abstract:We study the hydrodynamics of a system of agents who optimize either their individual utility (self-interest) or the collective welfare (cooperation). When agents act selfishly, their interactions are non-reciprocal, driving the system out of equilibrium; by contrast, purely altruistic dynamics restore reciprocity and yield an equilibrium-like description. We investigate how mixtures of these two behaviors shape the macroscopic properties of the liquid of agents. For highly rational agents, we find that introducing a small fraction of altruists can suppress the sub-optimal clustering induced by selfish dynamics. This phenomenon can be attributed to altruists localizing at interfaces and acting as effective surfactants, shedding a new light on earlier findings in fixed neighborhood-based models [Phys. Rev. Lett. \textbf{120}, 208301 (2018)]. When agents are boundedly rational, we introduce a well-mixed approximation that reduces the two-population model to a single effective scalar field theory. This allows us to leverage state-of-the-art tools from active matter to analytically characterize how altruism modifies surface tension and nucleation dynamics.

Valeyre, Sebastien; Aboura, Sofiane

doi: 10.48550/arxiv.2412.09394pmid: N/A

Abstract:Recently, LLMs (Large Language Models) have been adapted for time series prediction with significant success in pattern recognition. However, the common belief is that these models are not suitable for predicting financial market returns, which are known to be almost random. We aim to challenge this misconception through a counterexample. Specifically, we utilized the Chronos model from Ansari et al.(2024) and tested both pretrained configurations and fine-tuned supervised forecasts on the largest American single stocks using data from Guijarro-Ordonnez et al.(2022). We constructed a long/short portfolio, and the performance simulation indicates that LLMs can in reality handle time series that are nearly indistinguishable from noise, demonstrating an ability to identify inefficiencies amidst randomness and generate alpha. Finally, we compared these results with those of specialized models and smaller deep learning models, highlighting significant room for improvement in LLM performance to further enhance their predictive capabilities.

James, Nick; Menzies, Max

doi: 10.1016/j.physd.2025.134571pmid: N/A

Abstract:This paper studies the time-varying structure of the equity market with respect to market capitalization. First, we analyze the distribution of the 100 largest companies' market capitalizations over time, in terms of inequality, concentration at the top, and overall discrepancies in the distribution between different times. In the next section, we introduce a mathematical framework of linear and nonlinear functionals of time-varying portfolios. We apply this to study the market capitalization exposure and spread of optimal portfolios chosen by a Sharpe optimization procedure. These methods could be more widely used to study various measures of optimal portfolios and measure different aspects of market exposure while holding portfolios selected by an optimization routine that changes over time.

Ke, Zong; Yin, Yuchen

doi: 10.1109/icaice63571.2024.10864316pmid: N/A

Abstract:As the increasing application of AI in finance, this paper will leverage AI algorithms to examine tail risk and develop a model to alter tail risk to promote the stability of US financial markets, and enhance the resilience of the US economy. Specifically, the paper constructs a multivariate multilevel CAViaR model, optimized by gradient descent and genetic algorithm, to study the tail risk spillover between the US stock market, foreign exchange market and credit market. The model is used to provide early warning of related risks in US stocks, US credit bonds, etc. The results show that, by analyzing the direction, magnitude, and pseudo-impulse response of the risk spillover, it is found that the credit market's spillover effect on the stock market and its duration are both greater than the spillover effect of the stock market and the other two markets on credit market, placing credit market in a central position for warning of extreme risks. Its historical information on extreme risks can serve as a predictor of the VaR of other markets.

Hean, Oudom; Saha, Utsha; Saha, Binita

doi: 10.48550/arxiv.2412.19784pmid: N/A

Abstract:In recent years, Large Language Models (LLMs) have emerged as a transformative development in artificial intelligence (AI), drawing significant attention from industry and academia. Trained on vast datasets, these sophisticated AI systems exhibit impressive natural language processing and content generation capabilities. This paper explores the potential of LLMs to address key challenges in personal finance, focusing on the United States. We evaluate several leading LLMs, including OpenAI's ChatGPT, Google's Gemini, Anthropic's Claude, and Meta's Llama, to assess their effectiveness in providing accurate financial advice on topics such as mortgages, taxes, loans, and investments. Our findings show that while these models achieve an average accuracy rate of approximately 70%, they also display notable limitations in certain areas. Specifically, LLMs struggle to provide accurate responses for complex financial queries, with performance varying significantly across different topics. Despite these limitations, the analysis reveals notable improvements in newer versions of these models, highlighting their growing utility for individuals and financial advisors. As these AI systems continue to evolve, their potential for advancing AI-driven applications in personal finance becomes increasingly promising.

Yan, Ran; Zhou, Nan; Ma, Minda; Mao, Chao

doi: 10.48550/arxiv.2412.06360pmid: N/A

Abstract:As an emerging emitter poised for significant growth in space cooling demand, India requires comprehensive insights into historical emission trends and decarbonization performance to shape future low-carbon cooling strategies. By integrating a bottom-up demand resource energy analysis model and a top-down decomposition method, this study is the first to conduct a state-level analysis of carbon emission trends and the corresponding decarbonization efforts for residential space cooling in urban and rural India from 2000 to 2022. The results indicate that (1) the carbon intensity of residential space cooling in India increased by 292.4% from 2000 to 2022, reaching 513.8 kilograms of carbon dioxide per household. The net state domestic product per capita, representing income, emerged as the primary positive contributor. (2) The increase in carbon emissions from space cooling can be primarily attributed to the use of fans. While fan-based space cooling has nearly saturated Indian urban households, it is anticipated to persist as the primary cooling method in rural households for decades. (3) States with higher decarbonization potential are concentrated in two categories: those with high household income and substantial cooling appliance ownership and those with pronounced unmet cooling demand but low household income and hot climates. Furthermore, it is believed that promoting energy-efficient building designs can be prioritized to achieve affordable space cooling. Overall, this study serves as an effective foundation for formulating and promoting India's future cooling action plan, addressing the country's rising residential cooling demands and striving toward its net-zero goal by 2070.