In recent decades, companies have frequently adopted share repurchase programs to return capital to shareholders or for other strategic purposes, instructing investment banks to rapidly buy back shares on their behalf. When the executing institution is allowed to hedge its exposure, it encounters several challenges due to the intrinsic features of the product. Moreover, contractual clauses or market regulations on trading activity may make it infeasible to rely on Greeks. In this work, we address the hedging of these products by developing a machine-learning framework that determines the optimal execution of the buyback while explicitly accounting for the bank's actual trading capabilities. This unified treatment of execution and hedging yields substantial performance improvements, resulting in an optimized policy that provides a feasible and realistic hedging approach. The pricing of these programs can be framed in terms of the discount that banks offer to the client on the price at which the shares are delivered. Since, in our framework, risk measures serve as objective functions, we exploit the concept of indifference pricing to compute this discount, thereby capturing the actual execution performance.

The European Central Bank (ECB) is working on the "digital euro", an envisioned retail central bank digital currency for the Euro area. In this article, we take a closer look at the "digital euro FAQ", which provides answers to 26 frequently asked questions about the digital euro, and other published documents by the ECB on the topic. We question the provided answers based on our analysis of the current design in terms of privacy, technical feasibility, risks, costs and utility. In particular, we discuss the following key findings: (KF1) Central monitoring of all online digital euro transactions by the ECB threatens privacy even more than contemporary digital payment methods with segregated account databases. (KF2) The ECB's envisioned concept of a secure offline version of the digital euro offering full anonymity is in strong conflict with the actual history of hardware security breaches and mathematical evidence against it. (KF3) The legal and financial liabilities for the various parties involved remain unclear. (KF4) The design lacks well-specified economic incentives for operators as well as a discussion of its economic impact on merchants. (KF5) The ECB fails to identify tangible benefits the digital euro would create for society, in particular given that the online component of the proposed infrastructure mainly duplicates existing payment systems. (KF6) The design process has been exclusionary, with critical decisions being set in stone before public consultations. Alternative and open design ideas have not even been discussed by the ECB.

We show that the Markowitz portfolio is a scalar multiple of another portfolio which replaces the covariance with the second moment matrix, via simple application of the Sherman-Morrison identity. Moreover it is shown that when using conditional estimates of the first two moments, this "Sherman-Morrison-Markowitz" portfolio solves the standard unconditional portfolio optimization problems. We argue that in multi-period portfolio optimization problems it is more natural to replace variance and covariance with their uncentered counterparts. We extend the theory to deal with constraints in expectation, where we find a decomposition of squared effects into spanned and orthogonal components. Compared to the Markowitz portfolio, the Sherman-Morrison-Markowitz portfolio downlevers by a small amount that depends on the conditional squared maximal Sharpe ratio; the practical impact will be fairly small, however. We present some example use cases for the theory.

We introduce BASTION (Bayesian Adaptive Seasonality and Trend DecompositION), a flexible Bayesian framework for decomposing time series into trend and multiple seasonality components. We cast the decomposition as a penalized nonparametric regression and establish formal conditions under which the trend and seasonal components are uniquely identifiable, an issue only treated informally in the existing literature. BASTION offers three key advantages over existing decomposition methods: (1) accurate estimation of trend and seasonality amidst abrupt changes, (2) enhanced robustness against outliers and time-varying volatility, and (3) robust uncertainty quantification. We evaluate BASTION against established methods, including TBATS, STR, and MSTL, using both simulated and real-world datasets. By effectively capturing complex dynamics while accounting for irregular components such as outliers and heteroskedasticity, BASTION delivers a more nuanced and interpretable decomposition. To support further research and practical applications, BASTION is available as an R package at https://github.com/Jasoncho0914/BASTION

Market expectations about AI's economic impact may influence interest rates. Previous work has shown that US bond yields decline around the release of a sample of mostly proprietary AI models (Andrews and Farboodi 2025). I extend this analysis to include also open weight AI models that can be freely used and modified. I find long-term bond yields shift in opposite directions following the introduction of open versus closed models. Patterns are similar for treasuries, corporate bonds, and TIPS. The different movements suggest that that markets may anticipate open and closed AI advances to have different economic implications, and that the cumulative impact of AI releases on bond yields may be more muted.

Large-scale AI data center portfolios procure identical SKUs across geographically heterogeneous campuses, yet finance and operations require a single system-level 'world price' per SKU for budgeting and planning. A common practice is deployment-weighted blending of campus prices, which preserves total cost but can trigger Simpson-type aggregation failures: heterogeneous location mixes can reverse SKU rankings and distort decision signals. I formalize cost-preserving blended pricing under location heterogeneity and propose two practical operators that reconcile accounting identity with ranking robustness and production implementability. A two-way fixed-effects operator separates global SKU effects from campus effects and restores exact cost preservation via scalar normalization, providing interpretable decomposition and smoothing under mild missingness. A convex common-weight operator computes a single set of campus weights under accounting constraints to enforce a location-robust benchmark and prevent dominance reversals; I also provide feasibility diagnostics and a slack-based fallback for extreme mix conditions. Simulations and an AI data center OPEX illustration show substantial reductions in ranking violations relative to naive blending while maintaining cost accuracy, with scalable distributed implementation.

Hybrid-quantum classical optimization has emerged as a promising direction for addressing financial decision problems under current quantum hardware constraints. In this work we present a practical end-to-end portfolio optimization pipeline that combines (i) a continuous mean-variance and Sharpe-ratio formulation, (ii) a QUBO/CQM-based discrete asset selection stage solved using D-Wave's hybrid quantum annealing solver, (iii) classical convex optimization for computing optimal asset weights, and (iv) a quarterly rebalancing mechanism. Rather than claiming quantum advantage, our goal is to evaluate the feasibility and integration of these components within a deployable financial workflow. We empirically compare our hybrid pipeline against a fund manager in real time and indexes used in Indian stock market. The results indicate that the proposed framework can construct diversified portfolios and achieve competitive returns. We also report computational considerations and scalability observations drawn from the hybrid solver behaviour. While the experiments are limited to moderate sized portfolios dictated by current annealing hardware and QUBO embedding constraints, the study illustrates how quantum assisted selection and classical allocation can be combined coherently in a real-world setting. This work emphasizes methodological reproducibility and practical applicability, and aims to serve as a step toward larger-scale financial optimization workflows as quantum annealers continue to mature.

The declining provision of inertia by synchronous generators in modern power systems necessitates aggregating distributed energy resources (DERs) into virtual power plants (VPPs) to unlock their potential in delivering inertia and primary frequency response (IPFR) through ancillary service markets. To facilitate DER participation in the IPFR market, this paper proposes an aggregation model and market mechanism for VPPs participating in IPFR. First, an energy-reserve-IPFR market framework is developed, in which a VPP acts as an intermediary to coordinate heterogeneous DERs. Second, by taking into account the delay associated with inertial response, an optimization-based VPP aggregation method is introduced to encapsulate the IPFR process involving a variety of DERs. Third, an energy-reserve-IPFR market mechanism with VPP participation is introduced, aiming to minimize social costs, where stochastic deviations of renewable energy generation are explicitly modeled through chance-constrained reformulations, ensuring that the cleared energy, reserve, and IPFR schedules remain secure against forecast errors. Case studies on IEEE 30-bus and IEEE 118-bus systems show that the nadir and quasi-steady-state frequencies are reproduced by the VPP aggregation model with a mean absolute percentage error <= 0.03%, and the proposed market mechanism with VPP participation reduces the total system cost by approximately 40% and increases the net profit by about 30%.

Electricity price forecasting approaches generally fall into two categories: data-driven models, which learn from historical patterns, or fundamental models, which simulate market mechanisms. We propose a novel and highly efficient data-driven merit order model that integrates both paradigms. The model embeds the classical expert-based merit order as a nested special case, allowing all key parameters, such as plant efficiencies, bidding behavior, and available capacities, to be estimated directly from historical data, rather than assumed. We further enhance the model with critical embedded extensions such as hydro power, cross-border flows and corrections for underreported capacities, which considerably improve forecasting accuracy. Applied to the German day-ahead market, our model outperforms both classic fundamental and state-of-the-art machine learning models. It retains the interpretability of fundamental models, offering insights into marginal technologies, fuel switches, and dispatch patterns, elements which are typically inaccessible to black-box machine learning approaches. This transparency and high computational efficiency make it a promising new direction for electricity price modeling.

This paper addresses the question of how much to bid to maximize the profit when trading in two electricity markets: the hourly Day-Ahead Auction and the quarter-hourly Intraday Auction. For optimal coordinated bidding many price scenarios are examined, the own non-linear market impact is estimated by considering empirical supply and demand curves, and a number of trading strategies is used. Additionally, we provide theoretical results for risk neutral agents. The application study is conducted using the German market data, but the presented methods can be easily utilized with other two consecutive auctions. This paper contributes to the existing literature by evaluating the costs of electricity trading, i.e. the price impact and the transaction costs. The empirical results for the German EPEX market show that it is far more profitable to minimize the price impact rather than maximize the arbitrage.

This paper introduces MarketGAN, a factor-based generative framework for high-dimensional asset return generation under severe data scarcity. We embed an explicit asset-pricing factor structure as an economic inductive bias and generate returns as a single joint vector, thereby preserving cross-sectional dependence and tail co-movement alongside inter-temporal dynamics. MarketGAN employs generative adversarial learning with a temporal convolutional network (TCN) backbone, which models stochastic, time-varying factor loadings and volatilities and captures long-range temporal dependence. Using daily returns of large U.S. equities, we find that MarketGAN more closely matches empirical stylized facts of asset returns, including heavy-tailed marginal distributions, volatility clustering, leverage effects, and, most notably, high-dimensional cross-sectional correlation structures and tail co-movement across assets, than conventional factor-model-based bootstrap approaches. In portfolio applications, covariance estimates derived from MarketGAN-generated samples outperform those derived from other methods when factor information is at least weakly informative, demonstrating tangible economic value.

As LLMs increasingly function as economic agents, the specific mechanisms LLMs use to update their belief with heterogeneous signals remain opaque. We design experiments and develop a Behavioral Kalman Filter framework to quantify how LLM-based agents update expectations, acting as households or firm CEOs, update expectations when presented with individual and aggregate signals. The results from experiments and model estimation reveal four consistent patterns: (1) agents' weighting of priors and signals deviates from unity; (2) both household and firm CEO agents place substantially larger weights on individual signals compared to aggregate signals; (3) we identify a significant and negative interaction between concurrent signals, implying that the presence of multiple information sources diminishes the marginal weight assigned to each individual signal; and (4) expectation formation patterns differ significantly between household and firm CEO agents. Finally, we demonstrate that LoRA fine-tuning mitigates, but does not fully eliminate, behavioral biases in LLM expectation formation.

We present a study of the short-maturity asymptotics for VIX and European option prices in local-stochastic volatility models with compound Poisson jumps. Both out-of-the-money (OTM) and at-the-money (ATM) asymptotics are considered. The leading-order asymptotics are obtained in closed-form. We apply our results to three examples: the Eraker model, a Kou-type model, and a folded normal model. Numerical illustrations are provided for these three examples that show the accuracy of predictions based on the asymptotic results.

In this work, we investigate the market-making problem on a trading session in which a continuous phase on a limit order book is followed by a closing auction. Whereas standard optimal market-making models typically rely on terminal inventory penalties to manage end-of-day risk, ignoring the significant liquidity events available in closing auctions, we propose a Deep Q-Learning framework that explicitly incorporates this mechanism. We introduce a market-making framework designed to explicitly anticipate the closing auction, continuously refining the projected clearing price as the trading session evolves. We develop a generative stochastic market model to simulate the trading session and to emulate the market. Our theoretical model and Deep Q-Learning method is applied on the generator in two settings: (1) when the mid price follows a rough Heston model with generative data from this stochastic model; and (2) when the mid price corresponds to historical data of assets from the S&P 500 index and the performance of our algorithm is compared with classical benchmarks from optimal market making.

We propose a structural framework for the geometry of financial order books in which liquidity, supply, and demand are treated as emergent observables rather than primitive economic variables. The market is modeled as an inflationary relational system without assumed metric, temporal, or price coordinates. Observable quantities arise only through projection, implemented here via spectral embeddings of the graph Laplacian. A one-dimensional projection induces a price-like coordinate, while the projected density defines liquidity profiles around the mid price. Under a minimal single-scale hypothesis -- excluding intrinsic length scales beyond distance to the mid and finite visibility -- we show that projected supply and demand are constrained to gamma-like functional forms. In discrete data, this prediction translates into integrated-gamma cumulative profiles. We test these results using high-frequency Level~II data for several U.S. equities and find robust agreement across assets and intraday windows. Explicit comparison with alternative cumulative models using information criteria demonstrates a systematic preference for the integrated-gamma geometry. A minimal simulation of inflationary relational dynamics reproduces the same structure without invoking agent behavior or price formation mechanisms. These results indicate that key regularities of order-book liquidity reflect geometric constraints induced by observation rather than detailed microstructural dynamics. Supplementary Material is available at the arXiv submission.

With the reform of interest rate benchmarks, interbank offered rates (IBORs) like LIBOR have been replaced by risk-free rates (RFRs), such as the Secured Overnight Financing Rate (SOFR) in the U.S. and the Euro Short-Term Rate (\euro STR) in Europe. These rates exhibit characteristics like jumps and spikes that correspond to specific market events, driven by regulatory and liquidity constraints. To capture these characteristics, this paper considers a general short-rate model that incorporates discontinuities at fixed times with random sizes. Within this framework, we introduce a PDE-based approach for pricing interest rate derivatives and establish, under suitable assumptions, a Feynman-Kač representation for the solution. For affine models, we derive (quasi) closed-form solutions, while for the general case, we develop numerical methods to solve the resulting PDEs.

Stock recommendation is critical in Fintech applications, which leverage price series and alternative information to estimate future stock performance. Traditional time-series forecasting training often fails to capture stock trends and rankings simultaneously, which are essential factors for investors. To tackle this issue, we introduce a Multi-Task Learning (MTL) framework for stock recommendation, \textbf{M}omentum-\textbf{i}ntegrated \textbf{M}ulti-task \textbf{Stoc}k \textbf{R}ecommendation with Converge-based Optimization (\textbf{MiM-StocR}). To improve the model's ability to capture short-term trends, we incorporate a momentum line indicator in model training. To prioritize top-performing stocks and optimize investment allocation, we propose a listwise ranking loss function called Adaptive-k ApproxNDCG. Moreover, due to the volatility and uncertainty of the stock market, existing MTL frameworks face overfitting issues when applied to stock time series. To mitigate this issue, we introduce the Converge-based Quad-Balancing (CQB) method. We conducted extensive experiments on three stock benchmarks: SEE50, CSI 100, and CSI 300. MiM-StocR outperforms state-of-the-art MTL baselines across both ranking and profitability evaluations.

Recovery rate prediction plays a pivotal role in bond investment strategies by enhancing risk assessment, optimizing portfolio allocation, improving pricing accuracy, and supporting effective credit risk management. However, accurate forecasting remains challenging due to complex nonlinear dependencies, high-dimensional feature spaces, and limited sample sizes-conditions under which classical machine learning models are prone to overfitting. We propose a hybrid Quantum Machine Learning (QML) model with Amplitude Encoding, leveraging the unitarity constraint of Parametrized Quantum Circuits (PQC) and the exponential data compression capability of qubits. We evaluate the model on a global recovery rate dataset comprising 1,725 observations and 256 features from 1996 to 2023. Our hybrid method significantly outperforms both classical neural networks and QML models using Angle Encoding, achieving a lower Root Mean Squared Error (RMSE) of 0.228, compared to 0.246 and 0.242, respectively. It also performs competitively with ensemble tree methods such as XGBoost. While practical implementation challenges remain for Noisy Intermediate-Scale Quantum (NISQ) hardware, our quantum simulation and preliminary results on noisy simulators demonstrate the promise of hybrid quantum-classical architectures in enhancing the accuracy and robustness of recovery rate forecasting. These findings illustrate the potential of quantum machine learning in shaping the future of credit risk prediction.

In decentralized finance, any individual can pool their assets into an automated market maker (AMM) -- herein we focus on the constant product market maker (CPMM) -- in exchange for a claim on a fraction of future pool assets and fees earned from the market making operations. This position is represented by a liquidity token, whose prevailing on-chain price is effectively the initial deposited assets. Though this price is well-defined, we treat the liquidity token as a derivative position in the prices of the underlying assets for the CPMM in order to deduce risk-neutral pricing and hedging formulas, not dissimilar to the Black-Scholes result. Adopting this perspective, in a frictionless environment, hedging the CPMM liquidity token under fair valuation should produce a riskless process, which therefore grows at the risk-free rate, something that is not seen in empirical case studies under the prevailing price. With our novel pricing formula, we construct a method to calibrate a volatility to data which provides an updated (non-market) valuation which is consistent with the (near-continuous) replication strategy out-of-sample. We conclude with a discussion of novel AMM design considerations motivated by this derivative-pricing perspective.

We attempt to mitigate the persistent tradeoff between risk and return in medium- to long-term portfolio management. This paper proposes a novel LLM-guided no-regret portfolio allocation framework that integrates online learning dynamics, market sentiment indicators, and large language model (LLM)-based hedging to construct high-Sharpe ratio portfolios tailored for risk-averse investors and institutional fund managers. Our approach builds on a follow-the-leader approach, enriched with sentiment-based trade filtering and LLM-driven downside protection. Empirical results demonstrate that our method outperforms a SPY buy-and-hold baseline by 69% in annualized returns and 119% in Sharpe ratio.

Algorithmic trading relies on machine learning models to make trading decisions. Despite strong in-sample performance, these models often degrade when confronted with evolving real-world market regimes, which can shift dramatically due to macroeconomic changes-e.g., monetary policy updates or unanticipated fluctuations in participant behavior. We identify two challenges that perpetuate this mismatch: (1) insufficient robustness in existing policy against uncertainties in high-level market fluctuations, and (2) the absence of a realistic and diverse simulation environment for training, leading to policy overfitting. To address these issues, we propose a Bayesian Robust Framework that systematically integrates a macro-conditioned generative model with robust policy learning. On the data side, to generate realistic and diverse data, we propose a macro-conditioned GAN-based generator that leverages macroeconomic indicators as primary control variables, synthesizing data with faithful temporal, cross-instrument, and macro correlations. On the policy side, to learn robust policy against market fluctuations, we cast the trading process as a two-player zero-sum Bayesian Markov game, wherein an adversarial agent simulates shifting regimes by perturbing macroeconomic indicators in the macro-conditioned generator, while the trading agent-guided by a quantile belief network-maintains and updates its belief over hidden market states. The trading agent seeks a Robust Perfect Bayesian Equilibrium via Bayesian neural fictitious self-play, stabilizing learning under adversarial market perturbations. Extensive experiments on 9 financial instruments demonstrate that our framework outperforms 9 state-of-the-art baselines. In extreme events like the COVID, our method shows improved profitability and risk management, offering a reliable solution for trading under uncertain and shifting market dynamics.

This paper addresses the methodology for the quarterly estimation of Compensation of Employees paid by the General Government (GG) sector, in accordance with the European System of Accounts (ESA 2010). Due to the limited high-frequency data availability and the need to guarantee the consistency with annual constraints, quarterly estimation relies on indirect temporal disaggregation techniques. These methods use specific infra-annual indicators as proxies for the variables being estimated. The specific case of the quarterly estimation of Compensation of employees presents several additional challenges. Firstly, the information provided by the sources, based on cash or legal-accrual data, is elaborated to define indicators which respect the accrual ESA 2010 principle as the annual estimates, based on more compliant data sources such as final budgets of public entities. Secondly, at a quarterly level the extraordinary events - such as the recording of delayed collective bargaining agreements which result in arrears - have a strong impact on quarterly indicators, whereas their effect is mitigated at annual level. To attribute these flows to the period when the work is performed, multi-source data harmonization techniques are employed. Thirdly, to accurately reflect intra-annual dynamics, information is collected for specific groups of GG entities (e.g., regions and provinces) and aggregated into ESA 2010 GG sub-sectors (Central Government, Local Government, Social Security Funds) leading to three specific estimates. To validate temporal disaggregation models and ensure methodological rigor and data quality, statistical tests are applied throughout the process. The results confirm the effectiveness of this methodology in providing accurate and timely quarterly estimates of Compensation of employees for the GG sector, thereby supporting reliable short-term economic analysis and policy making.