Error bound for the asymptotic expansion of the Hartman-Watson integral ArXiv ID: 2504.04992 “View on arXiv” Authors: Unknown Abstract This note gives a bound on the error of the leading term of the $t\to 0$ asymptotic expansion of the Hartman-Watson distribution $θ(r,t)$ in the regime $rt=ρ$ constant. The leading order term has the form $θ(ρ/t,t)=\frac{“1”}{“2πt”}e^{"-\frac{1"}{“t”} (F(ρ)-π^2/2)} G(ρ) (1 + \vartheta(t,ρ))$, where the error term is bounded uniformly over $ρ$ as $|\vartheta(t,ρ)|\leq \frac{“1”}{“70”}t$. ...

Efficient Portfolio Selection through Preference Aggregation with Quicksort and the Bradley–Terry Model ArXiv ID: 2504.16093 “View on arXiv” Authors: Unknown Abstract How to allocate limited resources to projects that will yield the greatest long-term benefits is a problem that often arises in decision-making under uncertainty. For example, organizations may need to evaluate and select innovation projects with risky returns. Similarly, when allocating resources to research projects, funding agencies are tasked with identifying the most promising proposals based on idiosyncratic criteria. Finally, in participatory budgeting, a local community may need to select a subset of public projects to fund. Regardless of context, agents must estimate the uncertain values of a potentially large number of projects. Developing parsimonious methods to compare these projects, and aggregating agent evaluations so that the overall benefit is maximized, are critical in assembling the best project portfolio. Unlike in standard sorting algorithms, evaluating projects on the basis of uncertain long-term benefits introduces additional complexities. We propose comparison rules based on Quicksort and the Bradley–Terry model, which connects rankings to pairwise “win” probabilities. In our model, each agent determines win probabilities of a pair of projects based on his or her specific evaluation of the projects’ long-term benefit. The win probabilities are then appropriately aggregated and used to rank projects. Several of the methods we propose perform better than the two most effective aggregation methods currently available. Additionally, our methods can be combined with sampling techniques to significantly reduce the number of pairwise comparisons. We also discuss how the Bradley–Terry portfolio selection approach can be implemented in practice. ...

Information Leakages in the Green Bond Market ArXiv ID: 2504.03311 “View on arXiv” Authors: Unknown Abstract Public announcement dates are used in the green bond literature to measure equity market reactions to upcoming green bond issues. We find a sizeable number of green bond announcements were pre-dated by anonymous information leakages on the Bloomberg Terminal. From a candidate set of 2,036 ‘Bloomberg News’ and ‘Bloomberg First Word’ headlines gathered between 2016 and 2022, we identify 259 instances of green bond-related information being released before being publicly announced by the issuing firm. These pre-announcement leaks significantly alter the equity trading dynamics of the issuing firms over intraday and daily event windows. Significant negative abnormal returns and increased trading volumes are observed following news leaks about upcoming green bond issues. These negative investor reactions are concentrated amongst financial firms, and leaks that arrive pre-market or early in market trading. We find equity price movements following news leaks can be explained to a greater degree than following public announcements. Sectoral differences are also observed in the key drivers behind investor reactions to green bond leaks by non-financials (Tobin’s Q and free cash flow) and financials (ROA). Our results suggest that information leakages have a strong impact on market behaviour, and should be accounted for in green bond literature. Our findings also have broader ramifications for financial literature going forward. Privileged access to financially material information, courtesy of the ubiquitous use of Bloomberg Terminals by professional investors, highlights the need for event studies to consider wider sets of communication channels to confirm the date at which information first becomes available. ...

Mathematical Modeling of Option Pricing with an Extended Black-Scholes Framework ArXiv ID: 2504.03175 “View on arXiv” Authors: Unknown Abstract This study investigates enhancing option pricing by extending the Black-Scholes model to include stochastic volatility and interest rate variability within the Partial Differential Equation (PDE). The PDE is solved using the finite difference method. The extended Black-Scholes model and a machine learning-based LSTM model are developed and evaluated for pricing Google stock options. Both models were backtested using historical market data. While the LSTM model exhibited higher predictive accuracy, the finite difference method demonstrated superior computational efficiency. This work provides insights into model performance under varying market conditions and emphasizes the potential of hybrid approaches for robust financial modeling. ...

Convergence of the Markovian iteration for coupled FBSDEs via a differentiation approach ArXiv ID: 2504.02814 “View on arXiv” Authors: Unknown Abstract In this paper, we investigate the Markovian iteration method for solving coupled forward-backward stochastic differential equations (FBSDEs) featuring a fully coupled forward drift, meaning the drift term explicitly depends on both the forward and backward processes. An FBSDE system typically involves three stochastic processes: the forward process $X$, the backward process $Y$ representing the solution, and the $Z$ process corresponding to the scaled derivative of $Y$. Prior research by Bender and Zhang (2008) has established convergence results for iterative schemes dealing with $Y$-coupled FBSDEs. However, extending these results to equations with $Z$ coupling poses significant challenges, especially in uniformly controlling the Lipschitz constant of the decoupling fields across iterations and time steps within a fixed-point framework. To overcome this issue, we propose a novel differentiation-based method for handling the $Z$ process. This approach enables improved management of the Lipschitz continuity of decoupling fields, facilitating the well-posedness of the discretized FBSDE system with fully coupled drift. We rigorously prove the convergence of our Markovian iteration method in this more complex setting. Finally, numerical experiments confirm our theoretical insights, showcasing the effectiveness and accuracy of the proposed methodology. ...

On the Efficacy of Shorting Corporate Bonds as a Tail Risk Hedging Solution ArXiv ID: 2504.06289 “View on arXiv” Authors: Unknown Abstract United States (US) IG bonds typically trade at modest spreads over US Treasuries, reflecting the credit risk tied to a corporation’s default potential. During market crises, IG spreads often widen and liquidity tends to decrease, likely due to increased credit risk (evidenced by higher IG Credit Default Index spreads) and the necessity for asset holders like mutual funds to liquidate assets, including IG credits, to manage margin calls, bolster cash reserves, or meet redemptions. These credit and liquidity premia occur during market drawdowns and tend to move non-linearly with the market. The research herein refers to this non-linearity (during periods of drawdown) as downside convexity, and shows that this market behavior can effectively be captured through a short position established in IG Exchange Traded Funds (ETFs). The following document details the construction of three signals: Momentum, Liquidity, and Credit, that can be used in combination to signal entries and exits into short IG positions to hedge a typical active bond portfolio (such as PIMIX). A dynamic hedge initiates the short when signals jointly correlate and point to significant future hedged return. The dynamic hedge removes when the short position’s predicted hedged return begins to mean revert. This systematic hedge largely avoids IG Credit drawdowns, lowers absolute and downside risk, increases annualised returns and achieves higher Sortino ratios compared to the benchmark funds. The method is best suited to high carry, high active risk funds like PIMIX, though it also generalises to more conservative funds similar to DODIX. ...

Online Multivariate Regularized Distributional Regression for High-dimensional Probabilistic Electricity Price Forecasting ArXiv ID: 2504.02518 “View on arXiv” Authors: Unknown Abstract Probabilistic electricity price forecasting (PEPF) is vital for short-term electricity markets, yet the multivariate nature of day-ahead prices - spanning 24 consecutive hours - remains underexplored. At the same time, real-time decision-making requires methods that are both accurate and fast. We introduce an online algorithm for multivariate distributional regression models, allowing an efficient modelling of the conditional means, variances, and dependence structures of electricity prices. The approach combines multivariate distributional regression with online coordinate descent and LASSO-type regularization, enabling scalable estimation in high-dimensional covariate spaces. Additionally, we propose a regularized estimation path over increasingly complex dependence structures, allowing for early stopping and avoiding overfitting. In a case study of the German day-ahead market, our method outperforms a wide range of benchmarks, showing that modeling dependence improves both calibration and predictive accuracy. Furthermore, we analyse the trade-off between predictive accuracy and computational costs for batch and online estimation and provide an high-performing open-source Python implementation in the ondil package. ...

BASIR: Budget-Assisted Sectoral Impact Ranking – A Dataset for Sector Identification and Performance Prediction Using Language Models ArXiv ID: 2504.13189 “View on arXiv” Authors: Unknown Abstract Government fiscal policies, particularly annual union budgets, exert significant influence on financial markets. However, real-time analysis of budgetary impacts on sector-specific equity performance remains methodologically challenging and largely unexplored. This study proposes a framework to systematically identify and rank sectors poised to benefit from India’s Union Budget announcements. The framework addresses two core tasks: (1) multi-label classification of excerpts from budget transcripts into 81 predefined economic sectors, and (2) performance ranking of these sectors. Leveraging a comprehensive corpus of Indian Union Budget transcripts from 1947 to 2025, we introduce BASIR (Budget-Assisted Sectoral Impact Ranking), an annotated dataset mapping excerpts from budgetary transcripts to sectoral impacts. Our architecture incorporates fine-tuned embeddings for sector identification, coupled with language models that rank sectors based on their predicted performances. Our results demonstrate 0.605 F1-score in sector classification, and 0.997 NDCG score in predicting ranks of sectors based on post-budget performances. The methodology enables investors and policymakers to quantify fiscal policy impacts through structured, data-driven insights, addressing critical gaps in manual analysis. The annotated dataset has been released under CC-BY-NC-SA-4.0 license to advance computational economics research. ...

A cost of capital approach to determining the LGD discount rate ArXiv ID: 2503.23992 “View on arXiv” Authors: Unknown Abstract Loss Given Default (LGD) is a key risk parameter in determining a bank’s regulatory capital. During LGD-estimation, realised recovery cash flows are to be discounted at an appropriate rate. Regulatory guidance mandates that this rate should allow for the time value of money, as well as include a risk premium that reflects the “undiversifiable risk” within these recoveries. Having extensively reviewed earlier methods of determining this rate, we propose a new approach that is inspired by the cost of capital approach from the Solvency II regulatory regime. Our method involves estimating a market-consistent price for a portfolio of defaulted loans, from which an associated discount rate may be inferred. We apply this method to mortgage and personal loans data from a large South African bank. The results reveal the main drivers of the discount rate to be the mean and variance of these recoveries, as well as the bank’s cost of capital in excess of the risk-free rate. Our method therefore produces a discount rate that reflects both the undiversifiable risk of recovery recoveries and the time value of money, thereby satisfying regulatory requirements. This work can subsequently enhance the LGD-component within the modelling of both regulatory and economic capital. ...

Asymmetry in Distributions of Accumulated Gains and Losses in Stock Returns ArXiv ID: 2503.24241 “View on arXiv” Authors: Unknown Abstract We study decades-long historic distributions of accumulated S&P500 returns, from daily returns to those over several weeks. The time series of the returns emphasize major upheavals in the markets – Black Monday, Tech Bubble, Financial Crisis and Covid Pandemic – which are reflected in the tail ends of the distributions. De-trending the overall gain, we concentrate on comparing distributions of gains and losses. Specifically, we compare the tails of the distributions, which are believed to exhibit power-law behavior and possibly contain outliers. Towards this end we find confidence intervals of the linear fits of the tails of the complementary cumulative distribution functions on a log-log scale, as well as conduct a statistical U-test in order to detect outliers. We also study probability density functions of the full distributions of the returns with the emphasis on their asymmetry. The key empirical observations are that the mean of de-trended distributions increases near-linearly with the number of days of accumulation while the overall skew is negative – consistent with the heavier tails of losses – and depends little on the number of days of accumulation. At the same time the variance of the distributions exhibits near-perfect linear dependence on the number of days of accumulation, that is it remains constant if scaled to the latter. Finally, we discuss the theoretical framework for understanding accumulated returns. Our main conclusion is that the current state of theory, which predicts symmetric or near-symmetric distributions of returns cannot explain the aggregate of empirical results. ...