Quantitative Finance

Portfolio Management is the process of overseeing a group of investments, referred to as a portfolio, with the objective of achieving predetermined investment goals. Portfolio optimization is a key component that involves allocating the portfolio assets so as to maximize returns while minimizing risk taken. It is typically carried out by financial professionals who use a combination of quantitative techniques and investment expertise to make decisions about the portfolio allocation. Recent applications of Deep Reinforcement Learning (DRL) have shown promising results when used to optimize portfolio allocation by training model-free agents on historical market data. Many of these methods compare their results against basic benchmarks or other state-of-the-art DRL agents but often fail to compare their performance against traditional methods used by financial professionals in practical settings. One of the most commonly used methods for this task is Mean-Variance Portfolio Optimization (MVO), which uses historical time series information to estimate expected asset returns and covariances, which are then used to optimize for an investment objective. Our work is a thorough comparison between model-free DRL and MVO for optimal portfolio allocation. We detail the specifics of how to make DRL for portfolio optimization work in practice, also noting the adjustments needed for MVO. Backtest results demonstrate strong performance of the DRL agent across many metrics, including Sharpe ratio, maximum drawdowns, and absolute returns.

The present study investigates the numerical solution of Black-Scholes partial differential equation (PDE) for option valuation with multiple underlying assets. We develop a physics-informed (PI) machine learning algorithm based on a radial basis function neural network (RBFNN) that concurrently optimizes the network architecture and predicts the target option price. The physics-informed radial basis function neural network (PIRBFNN) combines the strengths of the traditional radial basis function collocation method and the physics-informed neural network machine learning approach to effectively solve PDE problems in the financial context. By employing a PDE residual-based technique to adaptively refine the distribution of hidden neurons during the training process, the PIRBFNN facilitates accurate and efficient handling of multidimensional option pricing models featuring non-smooth payoff conditions. The validity of the proposed method is demonstrated through a set of experiments encompassing a single-asset European put option, a double-asset exchange option, and a four-asset basket call option.

Large Language Models (LLMs) have shown strong capabilities in finance-oriented question answering, yet their evaluation on professional quantitative workflows remains fragmented and often stops at factual or document-grounded QA. We introduce QuantEval, a benchmark for evaluating whether LLMs can complete the compute--implement--validate loop required in quantitative finance. QuantEval contains 1,575 expert-validated instances across three complementary dimensions: (i) knowledge-based QA, (ii) quantitative mathematical reasoning, and (iii) quantitative strategy coding. The coding task is evaluated with a deterministic CTA-style backtesting framework that executes model-generated strategies and compares risk--return metrics against expert references, moving beyond syntax or template matching. We evaluate 13 open-source and proprietary LLMs, report prompt and reliability analyses, and observe substantial gaps relative to human experts, especially in multi-step reasoning and framework-constrained coding. We further conduct supervised fine-tuning and reinforcement learning experiments on domain-aligned data, showing that training can improve quantitative reasoning while also exposing trade-offs in factual recall. QuantEval releases the dataset, evaluation scripts, and full backtesting configuration to support reproducible research on LLMs for quantitative finance.

Signal decay and regime shifts pose recurring challenges for data-driven investment strategies in non-stationary markets, where conventional time-series and machine learning approaches often struggle to generalize beyond historical correlations. While large language models (LLMs) offer strong capabilities for processing unstructured information, their potential to support quantitative factor screening through explicit economic reasoning remains underexplored. Existing factor-based methods typically reduce alphas to numerical time series, overlooking the semantic rationale that determines when a factor is economically relevant. We present Alpha-R1, an RL-aligned LLM framework for context-aware alpha screening. Its core mechanism, semantic gating, evaluates each candidate factor's semantic profile against a dynamically constructed market state description, selecting a sparse subset of factors whose economic rationale aligns with current market conditions. The selection model is trained via group relative policy optimization (GRPO), using realized portfolio returns as the primary reward signal. Under a 12-month out-of-sample evaluation, Alpha-R1 achieves annualized returns of 47.87% on S&P 500 and 40.57% on CSI 300 with Sharpe ratios of 1.62 and 2.23. These results, obtained under a bounded candidate-pool evaluation protocol, provide evidence for second-stage semantic factor reranking in non-stationary markets. The full implementation and resources are available at https://github.com/FinStep-AI/Alpha-R1.

We develop a transparent, auditable large language model (LLM) pipeline for macro-financial stress testing. Structured prompting, with optional retrieval of country fundamentals and news, emits G7 macroeconomic scenarios (GDP growth, inflation, policy rate), which are converted into deviations from an IMF World Economic Outlook baseline and translated into portfolio losses through a three-channel PCA factor model. The macro-to-factor mapping is stipulated rather than estimated, so every tail-risk multiple is conditional on stated assumptions. Across 2,420 accepted scenarios from two model families and three runs, plus an unanchored-severity run and eight risk-layer ablations, we find three things. First, severity is inherited from scenario design, not generated by the model: prompt variant dominates every variance decomposition, removing the prompted severity bands makes GPT-5.6-luna's recession 1.6 pp milder, apparent country heterogeneity largely reflects the institutional baseline, and retrieval and news matter only where the prompt leaves magnitude free. Second, numerical severity and narrative severity are only weakly coupled. Third, GPT-5.6-luna follows its own arithmetic but anchors on prompted bands, whereas Llama-3.1-8B is four to seven times more dispersed and contradicts its own stated changes in 90% of cases. A repeat run differs at the scenario level yet agrees on aggregate multiples to within 0.007 times. LLM scenario generators are best used for narrative and sector elicitation around a prescribed severity path, not as autonomous calibrators of stress magnitude.

Modeling the dynamics of financial Limit Order Books (LOB) at the message level is challenging due to irregular event timing, rapid regime shifts, and the reactions of high-frequency traders to visible order flow. Previous LOB models require cumbersome data representations and lack adaptability outside their original tasks, leading us to introduce LOBERT, a general-purpose encoder-only foundation model for LOB data suitable for downstream fine-tuning. LOBERT adapts the original BERT architecture for LOB data by using a novel tokenization scheme that treats complete multi-dimensional messages as single tokens while retaining continuous representations of price, volume, and time. With these methods, LOBERT achieves leading performance in tasks such as predicting mid-price movements and next messages, while reducing the required context length compared to previous methods.

Large Language Models (LLMs) have recently been leveraged for asset pricing tasks and stock trading applications, enabling AI agents to generate investment decisions from unstructured financial data. However, most evaluations of LLM timing-based investing strategies are conducted on narrow timeframes and limited stock universes, overstating effectiveness due to survivorship and data-snooping biases. We critically assess their generalizability and robustness by proposing FINSABER, a backtesting framework evaluating timing-based strategies across longer periods and a larger universe of symbols. Systematic backtests over two decades and 100+ symbols reveal that previously reported LLM advantages deteriorate significantly under broader cross-section and over a longer-term evaluation. Our market regime analysis further demonstrates that LLM strategies are overly conservative in bull markets, underperforming passive benchmarks, and overly aggressive in bear markets, incurring heavy losses. These findings highlight the need to develop LLM strategies that are able to prioritise trend detection and regime-aware risk controls over mere scaling of framework complexity.

Quantum Support Vector Machine is a kernel-based approach to classification problems. We study the applicability of quantum kernels to financial data, specifically our self-curated Dhaka Stock Exchange (DSEx) Broad Index dataset. To the best of our knowledge, this is the first systematic study of quantum kernels applied to this dataset. Working within the empirical quantum advantage (EQA) framework of Krunic et al., we benchmark several quantum kernels against a classical RBF-kernel SVM baseline, propose the best-performing kernel for this dataset, and relate the observations to the Phase Space Terrain Ruggedness Index metric. We estimate the resources needed to carry out these investigations on a larger scale for future practitioners.

We propose the conditional moment kernel (CMK), a joint model of the conditional mean and covariance matrix of asset returns given their characteristics. A single kernel function of the characteristics gives the means and second moments of all returns. The implied covariance matrices are positive semidefinite for any number and composition of assets, so the model applies directly to unbalanced panels. Its estimation is a convex program whose size does not depend on the number of assets. A floor at the scale of the idiosyncratic noise keeps the estimated systematic covariance away from zero where the data cannot resolve it, and a trace penalty selects the number of factors. A closed form, the CMK estimator, approximates the solution. For fixed features and hyper-parameters, we prove identification, consistency and finite-sample bounds. In out-of-sample tests on US stocks from 1972 to 2021, the CMK estimator fits the conditional moments significantly better than instrumented principal component analysis (IPCA) with the same characteristics. Almost all of the gain is in the covariance matrix, and nonlinear functions of the characteristics add to it. The implied unconditionally mean--variance efficient portfolios earn annualized Sharpe ratios of 4.0 to 5.1 before costs, close to those of IPCA and declining over time.

Public data do not identify high-frequency trading (HFT), and standard proxies do not separate liquidity-supplying from liquidity-demanding strategies. We overcome this measurement challenge by training machine learning models on proprietary Nasdaq data to map observed HFT activity to public intraday variables. Applying this mapping, we generate daily measures of liquidity-supplying and liquidity-demanding HFT for all U.S. stocks from 2010 to 2023. The measures largely subsume standard proxies and capture time-series variation that those proxies miss. Using proprietary Euronext Paris data, we provide evidence that the approach generalizes across markets and remains predictive years after training. The 14-year panel lets us study HFT and market quality over time. Supply-side HFT is consistently associated with greater pre-announcement information acquisition, more informed trading, and lower bid-ask spreads, while demand-side HFT is associated with the opposite patterns. During COVID-19, HFT-supplied liquidity remained resilient and its association with lower spreads strengthened.

We show that a deep neural network (DNN) trained to construct a stochastic discount factor (SDF) admits an additive decomposition separating nonlinear characteristic discovery from the pricing rule that aggregates them. This decomposition yields a linear factor representation governed by the Portfolio Tangent Kernel (PTK), which summarizes the network's learned features. In population, the implied SDF converges to a ridge-regularized version of the true SDF, with the degree of regularization determined by spectral complexity. Empirically, using U.S. equity data, the PTK representation delivers economically and statistically significant performance gains, while rising spectral complexity imposes tighter limits on finite-sample pricing.

Classification outperforms regression across matched machine learning models in portfolio construction. A stacking ensemble of gradient boosted tree, random forest, and neural network yields a value-weighted annualized Sharpe ratio of 1.83 for classification and 1.11 for regression. This outperformance persists in multiclass settings, across subsamples, and after transaction costs. Spanning tests show that classification retains economically large alphas after we control for regression, whereas regression alphas shrink substantially once we control for classification. These results indicate that classification extracts more return information than matched regression. Our diagnostics trace classification's advantage to sharper and more precise separation of return deciles.