Volatility Calibration via Automatic Local Regression ArXiv ID: 2509.16334 “View on arXiv” Authors: Ruozhong Yang, Hao Qin, Charlie Che, Liming Feng Abstract Managing exotic derivatives requires accurate mark-to-market pricing and stable Greeks for reliable hedging. The Local Volatility (LV) model distinguishes itself from other pricing models by its ability to match observable market prices across all strikes and maturities with high accuracy. However, LV calibration is fundamentally ill-posed: finite market observables must determine a continuously-defined surface with infinite local volatility parameters. This ill-posed nature often causes spiky LV surfaces that are particularly problematic for finite-difference-based valuation, and induces high-frequency oscillations in solutions, thus leading to unstable Greeks. To address this challenge, we propose a pre-calibration smoothing method that can be integrated seamlessly into any LV calibration workflow. Our method pre-processes market observables using local regression that automatically minimizes asymptotic conditional mean squared error to generate denoised inputs for subsequent LV calibration. Numerical experiments demonstrate that the proposed pre-calibration smoothing yields significantly smoother LV surfaces and greatly improves Greek stability for exotic options with negligible additional computational cost, while preserving the LV model’s ability to fit market observables with high fidelity. ...

Adaptive and Regime-Aware RL for Portfolio Optimization ArXiv ID: 2509.14385 “View on arXiv” Authors: Gabriel Nixon Raj Abstract This study proposes a regime-aware reinforcement learning framework for long-horizon portfolio optimization. Moving beyond traditional feedforward and GARCH-based models, we design realistic environments where agents dynamically reallocate capital in response to latent macroeconomic regime shifts. Agents receive hybrid observations and are trained using constrained reward functions that incorporate volatility penalties, capital resets, and tail-risk shocks. We benchmark multiple architectures, including PPO, LSTM-based PPO, and Transformer PPO, against classical baselines such as equal-weight and Sharpe-optimized portfolios. Our agents demonstrate robust performance under financial stress. While Transformer PPO achieves the highest risk-adjusted returns, LSTM variants offer a favorable trade-off between interpretability and training cost. The framework promotes regime-adaptive, explainable reinforcement learning for dynamic asset allocation. ...

Dynamic Inverse Optimization under Drift and Shocks: Theory, Regret Bounds, and Applications ArXiv ID: 2509.14080 “View on arXiv” Authors: JINHO CHA Abstract The growing prevalence of drift and shocks in modern decision environments exposes a gap between classical optimization theory and real-world practice. Standard models assume fixed objectives, yet organizations from hospitals to power grids routinely adapt to shifting priorities, noisy data, and abrupt disruptions. To address this gap, this study develops a dynamic inverse optimization framework that recovers hidden, time-varying preferences from observed allocation trajectories. The framework unifies identifiability analysis with regret guarantees conditions are established for existence and uniqueness of recovered parameters, and sharp static and dynamic regret bounds are derived to characterize responsiveness to gradual drift and sudden shocks. Methodologically, a drift-aware estimator grounded in convex analysis and online learning theory is introduced, with finite-sample guarantees on recovery accuracy. Computational experiments in healthcare, energy, logistics, and finance reveal heterogeneous recovery patterns, ranging from rapid resilience to persistent vulnerability. Overall, dynamic inverse optimization emerges as both a theoretical contribution and a broadly applicable diagnostic tool for benchmarking resilience, uncovering hidden behavioral shifts, and guiding policy interventions in complex stochastic systems. ...

Fast and explicit European option pricing under tempered stable processes ArXiv ID: 2510.01211 “View on arXiv” Authors: Gaetano Agazzotti, Jean-Philippe Aguilar Abstract We provide series expansions for the tempered stable densities and for the price of European-style contracts in the exponential Lévy model driven by the tempered stable process. These formulas recover several popular option pricing models, and become particularly simple in some specific cases such as bilateral Gamma process and one-sided TS process. When compared to traditional Fourier pricing, our method has the advantage of being hyperparameter free. We also provide a detailed numerical analysis and show that our technique is competitive with state-of-the-art pricing methods. ...

Holdout cross-validation for large non-Gaussian covariance matrix estimation using Weingarten calculus ArXiv ID: 2509.13923 “View on arXiv” Authors: Lamia Lamrani, Benoît Collins, Jean-Philippe Bouchaud Abstract Cross-validation is one of the most widely used methods for model selection and evaluation; its efficiency for large covariance matrix estimation appears robust in practice, but little is known about the theoretical behavior of its error. In this paper, we derive the expected Frobenius error of the holdout method, a particular cross-validation procedure that involves a single train and test split, for a generic rotationally invariant multiplicative noise model, therefore extending previous results to non-Gaussian data distributions. Our approach involves using the Weingarten calculus and the Ledoit-Péché formula to derive the oracle eigenvalues in the high-dimensional limit. When the population covariance matrix follows an inverse Wishart distribution, we approximate the expected holdout error, first with a linear shrinkage, then with a quadratic shrinkage to approximate the oracle eigenvalues. Under the linear approximation, we find that the optimal train-test split ratio is proportional to the square root of the matrix dimension. Then we compute Monte Carlo simulations of the holdout error for different distributions of the norm of the noise, such as the Gaussian, Student, and Laplace distributions and observe that the quadratic approximation yields a substantial improvement, especially around the optimal train-test split ratio. We also observe that a higher fourth-order moment of the Euclidean norm of the noise vector sharpens the holdout error curve near the optimal split and lowers the ideal train-test ratio, making the choice of the train-test ratio more important when performing the holdout method. ...

Predictive Performance of LSTM Networks on Sectoral Stocks in an Emerging Market: A Case Study of the Pakistan Stock Exchange ArXiv ID: 2509.14401 “View on arXiv” Authors: Ahad Yaqoob, Syed M. Abdullah Abstract The application of deep learning models for stock price forecasting in emerging markets remains underexplored despite their potential to capture complex temporal dependencies. This study develops and evaluates a Long Short-Term Memory (LSTM) network model for predicting the closing prices of ten major stocks across diverse sectors of the Pakistan Stock Exchange (PSX). Utilizing historical OHLCV data and an extensive set of engineered technical indicators, we trained and validated the model on a multi-year dataset. Our results demonstrate strong predictive performance ($R^2 > 0.87$) for stocks in stable, high-liquidity sectors such as power generation, cement, and fertilizers. Conversely, stocks characterized by high volatility, low liquidity, or sensitivity to external shocks (e.g., global oil prices) presented significant forecasting challenges. The study provides a replicable framework for LSTM-based forecasting in data-scarce emerging markets and discusses implications for investors and future research. ...

DeltaHedge: A Multi-Agent Framework for Portfolio Options Optimization ArXiv ID: 2509.12753 “View on arXiv” Authors: Feliks Bańka, Jarosław A. Chudziak Abstract In volatile financial markets, balancing risk and return remains a significant challenge. Traditional approaches often focus solely on equity allocation, overlooking the strategic advantages of options trading for dynamic risk hedging. This work presents DeltaHedge, a multi-agent framework that integrates options trading with AI-driven portfolio management. By combining advanced reinforcement learning techniques with an ensembled options-based hedging strategy, DeltaHedge enhances risk-adjusted returns and stabilizes portfolio performance across varying market conditions. Experimental results demonstrate that DeltaHedge outperforms traditional strategies and standalone models, underscoring its potential to transform practical portfolio management in complex financial environments. Building on these findings, this paper contributes to the fields of quantitative finance and AI-driven portfolio optimization by introducing a novel multi-agent system for integrating options trading strategies, addressing a gap in the existing literature. ...

Income Disaster, Role of Income Support, and Optimal Retirement ArXiv ID: 2509.12874 “View on arXiv” Authors: Tae Ung Gang, Seyoung Park, Yong Hyun Shin Abstract This paper investigates the interactions among consumption/savings, investment, and retirement choices with income disaster. We consider low-income people who are exposed to income disaster so that they retire involuntarily when income disaster occurs. The government provides extra income support to low-income retirees who suffer from significant income gaps. We demonstrate that the decision to enter retirement in the event of income disaster depends crucially on the level of income support. In particular, we quantitatively identify a certain income support level below which the optimal decision is to delay retirement. This implies that availability of the government’s extra income support can be particularly important for the low-income people to achieve optimal retirement with income disaster. ...

Myopic Optimality: why reinforcement learning portfolio management strategies lose money ArXiv ID: 2509.12764 “View on arXiv” Authors: Yuming Ma Abstract Myopic optimization (MO) outperforms reinforcement learning (RL) in portfolio management: RL yields lower or negative returns, higher variance, larger costs, heavier CVaR, lower profitability, and greater model risk. We model execution/liquidation frictions with mark-to-market accounting. Using Malliavin calculus (Clark-Ocone/BEL), we derive policy gradients and risk shadow price, unifying HJB and KKT. This gives dual gap and convergence results: geometric MO vs. RL floors. We quantify phantom profit in RL via Malliavin policy-gradient contamination analysis and define a control-affects-dynamics (CAD) premium of RL indicating plausibly positive. ...

Bootstrapping Liquidity in BTC-Denominated Prediction Markets ArXiv ID: 2509.11990 “View on arXiv” Authors: Fedor Shabashev Abstract Prediction markets have gained adoption as on-chain mechanisms for aggregating information, with platforms such as Polymarket demonstrating demand for stablecoin-denominated markets. However, denominating in non-interest-bearing stablecoins introduces inefficiencies: participants face opportunity costs relative to the fiat risk-free rate, and Bitcoin holders in particular lose exposure to BTC appreciation when converting into stablecoins. This paper explores the case for prediction markets denominated in Bitcoin, treating BTC as a deflationary settlement asset analogous to gold under the classical gold standard. We analyse three methods of supplying liquidity to a newly created BTC-denominated prediction market: cross-market making against existing stablecoin venues, automated market making, and DeFi-based redirection of user trades. For each approach we evaluate execution mechanics, risks (slippage, exchange-rate risk, and liquidation risk), and capital efficiency. Our analysis shows that cross-market making provides the most user-friendly risk profile, though it requires active professional makers or platform-subsidised liquidity. DeFi redirection offers rapid bootstrapping and reuse of existing USDC liquidity, but exposes users to liquidation thresholds and exchange-rate volatility, reducing capital efficiency. Automated market making is simple to deploy but capital-inefficient and exposes liquidity providers to permanent loss. The results suggest that BTC-denominated prediction markets are feasible, but their success depends critically on the choice of liquidity provisioning mechanism and the trade-off between user safety and deployment convenience. ...