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on Risk Management |
| By: | Nendel, Max (Center for Mathematical Economics, Bielefeld University); Streicher, Jan (Center for Mathematical Economics, Bielefeld University) |
| Abstract: | In this paper, we deal with an axiomatic approach to default risk. We introduce the notion of a default risk measure, which generalizes the classical probability of default (PD), and allows to incorporate model risk in various forms. We discuss different properties and representations of default risk measures via monetary risk measures, families of related tail risk measures, and Choquet capacities. In a second step, we turn our focus on default risk measures, which are given as worst-case PDs and distorted PDs. The latter are frequently used in order to take into account model risk for the computation of capital requirements through risk-weighted assets (RWAs), as demanded by the Capital Requirement Regulation (CRR). In this context, we discuss the impact of different default risk measures and margins of conservatism on the amount of risk-weighted assets. |
| Keywords: | default risk measure, model uncertainty, probability of default, Choquet capacity, margin of conservatism, monetary risk measure, value at risk, risk-weighted assets |
| Date: | 2025–07–18 |
| URL: | https://d.repec.org/n?u=RePEc:bie:wpaper:725 |
| By: | De Vecchi, Corrado (Center for Mathematical Economics, Bielefeld University); Nendel, Max (Center for Mathematical Economics, Bielefeld University); Streicher, Jan (Center for Mathematical Economics, Bielefeld University) |
| Abstract: | In this paper, we study dependence uncertainty and the resulting effects on tail risk measures, which play a fundamental role in modern risk management. We introduce the notion of a regular dependence measure, defined on multi-marginal couplings, as a generalization of well-known correlation statistics such as the Pearson correlation. The first main result states that even an arbitrarily small positive dependence between losses can result in perfectly correlated tails beyond a certain threshold and seemingly complete independence before this threshold. In a second step, we focus on the aggregation of individual risks with known marginal distributions by means of arbitrary nondecreasing left-continuous aggregation functions. In this context, we show that under an arbitrarily small positive dependence, the tail risk of the aggregate loss might coincide with the one of perfectly correlated losses. A similar result is derived for expectiles under mild conditions. In a last step, we discuss our results in the context of credit risk, analyzing the potential effects on the value at risk for weighted sums of Bernoulli distributed losses. |
| Keywords: | Dependence uncertainty, dependence measure, risk aggregation, multimarginal coupling, copula, tail event, tail risk measure, value at risk, expectile |
| Date: | 2025–08–15 |
| URL: | https://d.repec.org/n?u=RePEc:bie:wpaper:739 |
| By: | Georgios I. Papayiannis; Georgios Psarrakos |
| Abstract: | This paper proposes a novel perspective on the relationship between Value at Risk (VaR) and Expected Shortfall (ES) by employing the mixing framework of Flexible Expected Shortfall (FES) to construct coherent representations of VaR. The methodology enables a reinterpretation of VaR within a coherent risk measure framework, thereby addressing well-known limitations of VaR, including non-subadditivity and insensitivity to tail risk. A central feature of the framework is the flexibility parameter inherent in FES, which captures salient distributional properties of the underlying risk profile. This parameter is formalized as the $\theta$-index, a normalized measure designed to reflect tail heaviness. Theoretical properties of the $\theta$-index are examined, and its relevance to risk assessment is established. Furthermore, risk capital allocation is analyzed using the Euler principle, facilitating consistent and meaningful marginal attribution. The practical implications of the approach are illustrated through appropriate simulation studies and an empirical analysis based on an insurance loss dataset with pronounced heavy-tailed characteristics. |
| Date: | 2025–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2507.13562 |
| By: | Rehim Kılıç |
| Abstract: | This paper fills an important gap in the volatility forecasting literature by comparing a broad suite of machine learning (ML) methods with both linear and nonlinear econometric models using high-frequency realized volatility (RV) data for the S&P 500. We evaluate ARFIMA, HAR, regime-switching HAR models (THAR, STHAR, MSHAR), and ML methods including Extreme Gradient Boosting, deep feed-forward neural networks, and recurrent networks (BRNN, LSTM, LSTM-A, GRU). Using rolling forecasts from 2006 onward, we find that regime-switching models—particularly THAR and STHAR—consistently outperform ML and linear models, especially when predictors are limited. These models also deliver more accurate risk forecasts and higher realized utility. While ML models capture some nonlinear patterns, they offer no consistent advantage over simpler, interpretable alternatives. Our findings highlight the importance of modeling regime changes through transparent econometric tools, especially in real-world applications where predictor availability is sparse and model interpretability is critical for risk management and portfolio allocation. |
| Keywords: | Realized volatility; Machine learning; Regime-switching; Nonlinearity; VaR; forecasting |
| JEL: | C10 C50 G11 G15 |
| Date: | 2025–08–08 |
| URL: | https://d.repec.org/n?u=RePEc:fip:fedgfe:2025-61 |
| By: | Kupper, Michael (Center for Mathematical Economics, Bielefeld University); Nendel, Max (Center for Mathematical Economics, Bielefeld University); Sgarabottolo, Alessandro (Center for Mathematical Economics, Bielefeld University) |
| Abstract: | In this paper, we study convex risk measures with weak optimal transport penalties. In a first step, we show that these risk measures allow for an explicit representation via a nonlinear transform of the loss function. In a second step, we discuss computational aspects related to the nonlinear transform as well as approximations of the risk measures using, for example, neural networks. Our setup comprises a variety of examples, such as classical optimal transport penalties, parametric families of models, uncertainty on path spaces, moment constrains, and martingale constraints. In a last step, we show how to use the theoretical results for the numerical computation of worstcase losses in an insurance context and no-arbitrage prices of European contingent claims after quoted maturities in a model-free setting. |
| Keywords: | Risk measure, weak optimal transport, neural network, model uncertainty, martingale optimal transport |
| Date: | 2025–08–14 |
| URL: | https://d.repec.org/n?u=RePEc:bie:wpaper:734 |
| By: | Biswarup Chakraborty |
| Abstract: | Portfolio optimization has long been dominated by covariance-based strategies, such as the Markowitz Mean-Variance framework. However, these approaches often fail to ensure a balanced risk structure across assets, leading to concentration in a few securities. In this paper, we introduce novel risk measures grounded in the equal-correlation portfolio strategy, aiming to construct portfolios where each asset maintains an equal correlation with the overall portfolio return. We formulate a mathematical optimization framework that explicitly controls portfolio-wide correlation while preserving desirable risk-return trade-offs. The proposed models are empirically validated using historical stock market data. Our findings show that portfolios constructed via this approach demonstrate superior risk diversification and more stable returns under diverse market conditions. This methodology offers a compelling alternative to conventional diversification techniques and holds practical relevance for institutional investors, asset managers, and quantitative trading strategies. |
| Date: | 2025–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2508.03704 |
| By: | Andres Mauricio Molina Barreto |
| Abstract: | Copula-based Conditional Value at Risk (CCVaR) is defined as an alternative version of the classical Conditional Value at Risk (CVaR) for multivariate random vectors intended to be real-valued. We aim to generalize CCVaR to several dimensions (d>=2) when the dependence structure is given by an Archimedean copula. While previous research focused on the bivariate case, leaving the multivariate version unexplored, an almost closed-form expression for CCVaR under an Archimedean copula is derived. The conditions under which this risk measure satisfies coherence are then examined. Finally, numerical experiments based on real data are conducted to estimate CCVaR, and the results are compared with classical measures of Value at Risk (VaR) and Conditional Value at Risk (CVaR). |
| Date: | 2025–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2508.16132 |
| By: | Ayush Jha; Abootaleb Shirvani; Ali M. Jaffri; Svetlozar T. Rachev; Frank J. Fabozzi |
| Abstract: | This paper develops a unified framework that integrates behavioral distortions into rational portfolio optimization by extracting implied probability weighting functions (PWFs) from optimal portfolios modeled under Gaussian and Normal-Inverse-Gaussian (NIG) return distributions. Using DJIA constituents, we construct mean-CVaR99 frontiers, alongwith Sharpe- and CVaR-maximizing portfolios, and estimate PWFs that capture nonlinear beliefs consistent with fear and greed. We show that increasing tail fatness amplifies these distortions and that shifts in the term structure of risk-free rates alter their curvature. The results highlight the importance of jointly modeling return asymmetry and belief distortions in portfolio risk management and capital allocation under extreme-risk environments. |
| Date: | 2025–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2507.04208 |
| By: | Monaco, Andrea (Center for Mathematical Economics, Bielefeld University); Perrotta, Adamaria (Center for Mathematical Economics, Bielefeld University); Sgarabottolo, Alessandro (Center for Mathematical Economics, Bielefeld University) |
| Abstract: | We analyze the price behavior of Bermudan swaption portfolios used for hedging prepayment-driven interest rate risks in loan portfolios. We evaluate a variety of swaption portfolios across maturities and prepayment rates under various market conditions. Our findings reveal the existence of a parametric relation between swaption portfolio prices and the characteristics of the hedged loan. This relationship holds across different market conditions and valuation models, suggesting that one can swiftly adjust a swaption-based hedging strategy as loan portfolio characteristics evolve. This parametric approach allows financial institutions to reduce costs when assessing prepayment risks in their loan portfolios. |
| Keywords: | swaptions, prepayment risk, option pricing, interest rates, parametric approach, model risk |
| Date: | 2025–08–14 |
| URL: | https://d.repec.org/n?u=RePEc:bie:wpaper:729 |
| By: | Juchan Kim; Inwoo Tae; Yongjae Lee |
| Abstract: | Portfolio optimization constitutes a cornerstone of risk management by quantifying the risk-return trade-off. Since it inherently depends on accurate parameter estimation under conditions of future uncertainty, the selection of appropriate input parameters is critical for effective portfolio construction. However, most conventional statistical estimators and machine learning algorithms determine these parameters by minimizing mean-squared error (MSE), a criterion that can yield suboptimal investment decisions. In this paper, we adopt decision-focused learning (DFL) - an approach that directly optimizes decision quality rather than prediction error such as MSE - to derive the global minimum-variance portfolio (GMVP). Specifically, we theoretically derive the gradient of decision loss using the analytic solution of GMVP and its properties regarding the principal components of itself. Through extensive empirical evaluation, we show that prediction-focused estimation methods may fail to produce optimal allocations in practice, whereas DFL-based methods consistently deliver superior decision performance. Furthermore, we provide a comprehensive analysis of DFL's mechanism in GMVP construction, focusing on its volatility reduction capability, decision-driving features, and estimation characteristics. |
| Date: | 2025–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2508.10776 |
| By: | Grzegorz Dudek; Witold Orzeszko; Piotr Fiszeder |
| Abstract: | Cryptocurrency markets are characterized by extreme volatility, making accurate forecasts essential for effective risk management and informed trading strategies. Traditional deterministic (point) forecasting methods are inadequate for capturing the full spectrum of potential volatility outcomes, underscoring the importance of probabilistic approaches. To address this limitation, this paper introduces probabilistic forecasting methods that leverage point forecasts from a wide range of base models, including statistical (HAR, GARCH, ARFIMA) and machine learning (e.g. LASSO, SVR, MLP, Random Forest, LSTM) algorithms, to estimate conditional quantiles of cryptocurrency realized variance. To the best of our knowledge, this is the first study in the literature to propose and systematically evaluate probabilistic forecasts of variance in cryptocurrency markets based on predictions derived from multiple base models. Our empirical results for Bitcoin demonstrate that the Quantile Estimation through Residual Simulation (QRS) method, particularly when applied to linear base models operating on log-transformed realized volatility data, consistently outperforms more sophisticated alternatives. Additionally, we highlight the robustness of the probabilistic stacking framework, providing comprehensive insights into uncertainty and risk inherent in cryptocurrency volatility forecasting. This research fills a significant gap in the literature, contributing practical probabilistic forecasting methodologies tailored specifically to cryptocurrency markets. |
| Date: | 2025–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2508.15922 |
| By: | Barbara D\"om\"ot\"or; Ferenc Ill\'es |
| Abstract: | Banks are required to use long-term default probabilities (PDs) of their portfolios when calculating credit risk capital under internal ratings-based (IRB) models. However, the calibration models and historical data typically reflect prevailing market conditions. According to Basel recommendations, averaging annual PDs over a full economic cycle should yield the long-term PD. In practice, the available data are often temporally incomplete - even for high-risk portfolios. In this paper, we present a method for the simultaneous calibration of long-term PDs across all sub-portfolios, based on the single risk factor model embedded in the Basel framework. The method is suitable even for smaller, budget-constrained institutions, as it relies exclusively on the bank's own default data. A complete dataset is not required - not even for any individual sub-portfolio - as the only prerequisite is the presence of overlapping data before and after the missing values, a mild condition that is typically met in practical situations. |
| Date: | 2025–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2508.15651 |
| By: | Milan Pontiggia (MAGEFI - University of Bordeaux, France) |
| Abstract: | We assess the applicability of rough volatility models to Bitcoin realised volatility using the normalised p-variation framework of Cont and Das (2024). Applying this model free estimator to high-frequency Bitcoin data from 2017 to 2024 across multiple sampling resolutions, we find that the normalised statistic remains strictly negative throughout, precluding the estimation of a valid roughness index. Stationarity tests and robustness checks reveal no significant evidence of non-stationarity or structural breaks as explanatory factors. Instead, convergent evidence from three complementary diagnostics, namely multifractal detrended fluctuation analysis, log-log moment scaling, and wavelet leaders, reveals a multifractal structure in Bitcoin volatility. This scale-dependent behaviour violates the homogeneity assumptions underlying rough volatility estimation and accounts for the estimator's systematic failure. These findings suggest that while rough volatility models perform well in traditional markets, they are structurally misaligned with the empirical features of Bitcoin volatility. |
| Date: | 2025–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2507.00575 |
| By: | Zhangying Li (Economics and Management School, Wuhan University); O-Chia Chuang (School of Digital Economics, Hubei University of Economics); Rangan Gupta (Department of Economics, University of Pretoria); Elie Bouri (School of Business, Lebanese American University, Lebanon) |
| Abstract: | Accurately predicting the Value-at-Risk (VaR) in commodity markets is crucial for risk management, yet the volatility and cyclicality of commodity prices pose significant challenges. This paper innovatively incorporates the information content of the Global Supply Chain Pressure Index (GSCPI) and the Global Economic Conditions Index (GECON) into the quantile Genaralized Autoregressive Conditional Heteroskedasticty-Mixed Data Sampling (GARCH-MIDAS) framework to address the issue of mismatched data frequencies, and explores the impact of these monthly indicators on daily commodity returns volatility. We find that the MIDAS framework significantly outperforms the conditional autoregressive VaR by regression quantiles (CAViaR) model, with asymmetric models showing superior performance. Both GSCPI and GECON exhibit strong explanatory power for VaR forecasting, highlighting the important influence of global supply and demand conditions on returns volatility of the overall commodity market, as well as its various sub-sectors. |
| Keywords: | VaR predictions, Quantiles-based mixed-frequency models, Commodity market |
| JEL: | C32 C53 E23 E32 Q02 |
| Date: | 2025–08 |
| URL: | https://d.repec.org/n?u=RePEc:pre:wpaper:202528 |
| By: | Beißner, Patrick (Center for Mathematical Economics, Bielefeld University); Werner, Jan (Center for Mathematical Economics, Bielefeld University) |
| Abstract: | The analysis of optimal risk sharing has been thus far largely restricted to non-expected utility models with concave utility functions, where concavity is an expression of ambiguity aversion and/or risk aversion. This paper extends the analysis to $\alpha$-maxmin expected utility, Choquet expected utility, and Cumulative Prospect Theory, which accommodate ambiguity seeking and risk seeking attitudes. We introduce a novel methodology of quasidifferential calculus of Demyanov and Rubinov (1986, 1992) and argue that it is particularly well-suited for the analysis of these three classes of utility functions which are neither concave nor differentiable. We provide characterizations of quasidifferentials of these utility functions, derive first-order conditions for Pareto optimal allocations under uncertainty, and analyze implications of these conditions for risk sharing with and without aggregate risk. |
| Keywords: | quasidifferential calculus, ambiguity, Pareto optimality, $\alpha$-MaxMin expected utility, Choquet expected utility, rank-dependent expected utility, Cumulative Prospect Theory |
| Date: | 2025–07–18 |
| URL: | https://d.repec.org/n?u=RePEc:bie:wpaper:722 |
| By: | Xiangyu Han; Yijun Hu; Ran Wang; Linxiao Wei |
| Abstract: | In this paper, by proposing two new kinds of distributional uncertainty sets, we explore robustness of distortion risk measures against distributional uncertainty. To be precise, we first consider a distributional uncertainty set which is characterized solely by a ball determined by general Wasserstein distance centered at certain empirical distribution function, and then further consider additional constraints of known first moment and any other higher moment of the underlying loss distribution function. Under the assumption that the distortion function is strictly concave and twice differentiable, and that the underlying loss random variable is non-negative and bounded, we derive closed-form expressions for the distribution functions which maximize a given distortion risk measure over the distributional uncertainty sets respectively. Moreover, we continue to study the general case of a concave distortion function and unbounded loss random variables. Comparisons with existing studies are also made. Finally, we provide a numerical study to illustrate the proposed models and results. Our work provides a novel generalization of several known achievements in the literature. |
| Date: | 2025–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2508.10682 |
| By: | Theodore Kapopoulos (Athens University of Economics and Business - Department of Accounting and Finance); Dimitrios Anastasiou (Athens University of Economics and Business - Department of Business Administration); Steven Ongena (University of Zurich - Department Finance; Swiss Finance Institute; KU Leuven; NTNU Business School; Centre for Economic Policy Research (CEPR)); Athanasios Sakkas (Athens University of Economics and Business - Department of Accounting and Finance) |
| Abstract: | We investigate the relationship between global geopolitical risk and bank deposit flows across a wide panel of European countries. Motivated by the pivotal role of deposit stability for financial intermediation and systemic resilience, we explore whether geopolitical shocks alter depositors' portfolio choices. Using quarterly country-level data and employing the Geopolitical Risk Index (GPR) of Caldara and Iacoviello (2022) along with its sub-indices (GPR Acts and GPR Threats), we document that rising global geopolitical risk significantly increases aggregate bank deposits. Specifically, a one-standard-deviation increase in geopolitical risk is associated with an average rise of €13.3 billion in household deposits and €5.6 billion in corporate deposits, highlighting the sizable financial reallocation triggered by global uncertainty. This positive effect is channelled through a reallocation from riskier assets to deposits, with a stronger reaction observed among households compared to firms. Our findings suggest that bank deposits act as a safe-haven asset in periods of heightened global tensions, complementing the flight-to-safety phenomenon documented in sovereign bond markets. The results have important implications for financial stability analysis, monetary policy transmission and banks' liquidity risk management under geopolitical stress. |
| Keywords: | bank deposit flows, geopolitical risk, financial instability |
| JEL: | G4 G21 F51 |
| Date: | 2025–07 |
| URL: | https://d.repec.org/n?u=RePEc:chf:rpseri:rp2564 |
| By: | Nendel, Max (Center for Mathematical Economics, Bielefeld University); Sgarabottolo, Alessandro (Center for Mathematical Economics, Bielefeld University) |
| Abstract: | In this paper, we explore a static setting for the assessment of risk in the context of mathematical finance and actuarial science that takes into account model uncertainty in the distribution of a possibly infinite-dimensional risk factor. We study convex risk functionals that incorporate a safety margin with respect to nonparametric uncertainty by penalizing perturbations from a given baseline model using Wasserstein distance. We investigate to which extent this form of probabilistic imprecision can be approximated by restricting to a parametric family of models. The particular form of the parametrization allows to develop numerical methods based on neural networks, which give both the value of the risk functional and the worst-case perturbation of the reference measure. Moreover, we consider additional constraints on the perturbations, namely, mean and martingale constraints. We show that, in both cases, under suitable conditions on the loss function, it is still possible to estimate the risk functional by passing to a parametric family of perturbed models, which again allows for numerical approximations via neural networks. |
| Keywords: | Risk measure, model uncertainty, Wasserstein distance, martingale optimal transport, parametric estimation, neural network, measurable direction of steepest ascent |
| Date: | 2025–07–18 |
| URL: | https://d.repec.org/n?u=RePEc:bie:wpaper:724 |
| By: | Priyanka Chudasama; Srikanth Krishnan Iyer |
| Abstract: | Hawkes processes were first introduced to obtain microscopic models for the rough volatility observed in asset prices. Scaling limits of such processes leads to the rough-Heston model that describes the macroscopic behavior. Blanc et al. (2017) show that Time-reversal asymmetry (TRA) or the Zumbach effect can be modeled using Quadratic Hawkes (QHawkes) processes. Dandapani et al. (2021) obtain a super-rough-Heston model as scaling limit of QHawkes processes in the case where the impact of buying and selling actions are symmetric. To model asymmetry in buying and selling actions, we propose a bivariate QHawkes process and derive a super-rough-Heston model as scaling limits for the price process in the stable and near-unstable regimes that preserves TRA. A new feature of the limiting process in the near-unstable regime is that the two driving Brownian motions exhibit a stochastic covariation that depends on the spot volatility. |
| Date: | 2025–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2508.16566 |
| By: | Fay\c{c}al Djebari; Kahina Mehidi; Khelifa Mazouz; Philipp Otto |
| Abstract: | This paper examines several network-based volatility models for oil prices, capturing spillovers among OPEC oil-exporting countries by embedding novel network structures into ARCH-type models. We apply a network-based log-ARCH framework that incorporates weight matrices derived from time-series clustering and model-implied distances into the conditional variance equation. These weight matrices are constructed from return data and standard multivariate GARCH model outputs (CCC, DCC, and GO-GARCH), enabling a comparative analysis of volatility transmission across specifications. Through a rolling-window forecast evaluation, the network-based models demonstrate competitive forecasting performance relative to traditional specifications and uncover intricate spillover effects. These results provide a deeper understanding of the interconnectedness within the OPEC network, with important implications for financial risk assessment, market integration, and coordinated policy among oil-producing economies. |
| Date: | 2025–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2507.15046 |
| By: | Arno Botha; Tanja Verster |
| Abstract: | Under the International Financial Reporting Standards (IFRS) 9, credit losses ought to be recognised timeously and accurately. This requirement belies a certain degree of dynamicity when estimating the constituent parts of a credit loss event, most notably the probability of default (PD). It is notoriously difficult to produce such PD-estimates at every point of loan life that are adequately dynamic and accurate, especially when considering the ever-changing macroeconomic background. In rendering these lifetime PD-estimates, the choice of modelling technique plays an important role, which is why we first review a few classes of techniques, including the merits and limitations of each. Our main contribution however is the development of an in-depth and data-driven tutorial using a particular class of techniques called discrete-time survival analysis. This tutorial is accompanied by a diverse set of reusable diagnostic measures for evaluating various aspects of a survival model and the underlying data. A comprehensive R-based codebase is further contributed. We believe that our work can help cultivate common modelling practices under IFRS 9, and should be valuable to practitioners, model validators, and regulators alike. |
| Date: | 2025–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2507.15441 |
| By: | Dirk Schoenmaker; Willem Schramade |
| Abstract: | Our model provides a bird’s eye view of a country’s exposure to transition |
| Date: | 2025–08 |
| URL: | https://d.repec.org/n?u=RePEc:bre:wpaper:node_11190 |
| By: | Tim J. Boonen; Engel John C. Dela Vega; Bin Zou |
| Abstract: | This paper considers an insurer with two collaborating business lines, and the risk exposure of each line follows a diffusion risk model. The manager of the insurer makes three decisions for each line: (i) dividend payout, (ii) (proportional) reinsurance coverage, and (iii) capital injection (from one line into the other). The manager seeks an optimal dividend, reinsurance, and capital injection strategy to maximize the expected weighted sum of the total dividend payments until the first ruin. We completely solve this problem and obtain the value function and optimal strategies in closed form. We show that the optimal dividend strategy is a threshold strategy, and the more important line always has a lower threshold to pay dividends. The optimal proportion of risk ceded to the reinsurer is decreasing with respect to the aggregate reserve level for each line, and capital injection is only used to prevent the ruin of a business line. Finally, numerical examples are presented to illustrate the impact of model parameters on the optimal strategies. |
| Date: | 2025–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2508.08130 |
| By: | Guilherme V. Moura; Andr\'e P. Santos; Hudson S. Torrent |
| Abstract: | Machine learning (ML) methods have been successfully employed in identifying variables that can predict the equity premium of individual stocks. In this paper, we investigate if ML can also be helpful in selecting variables relevant for optimal portfolio choice. To address this question, we parameterize minimum-variance portfolio weights as a function of a large pool of firm-level characteristics as well as their second-order and cross-product transformations, yielding a total of 4, 610 predictors. We find that the gains from employing ML to select relevant predictors are substantial: minimum-variance portfolios achieve lower risk relative to sparse specifications commonly considered in the literature, especially when non-linear terms are added to the predictor space. Moreover, some of the selected predictors that help decreasing portfolio risk also increase returns, leading to minimum-variance portfolios with good performance in terms of Shape ratios in some situations. Our evidence suggests that ad-hoc sparsity can be detrimental to the performance of minimum-variance characteristics-based portfolios. |
| Date: | 2025–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2508.14986 |
| By: | Weilong Liu; Yanchu Liu |
| Abstract: | The comovement phenomenon in financial markets creates decision scenarios with positively correlated asset returns. This paper addresses covariance matrix estimation under such conditions, motivated by observations of significant positive correlations in factor-sorted portfolio monthly returns. We demonstrate that fine-tuning eigenvectors linked to weak factors within rotation-equivariant frameworks produces well-conditioned covariance matrix estimates. Our Eigenvector Rotation Shrinkage Estimator (ERSE) pairwise rotates eigenvectors while preserving orthogonality, equivalent to performing multiple linear shrinkage on two distinct eigenvalues. Empirical results on factor-sorted portfolios from the Ken French data library demonstrate that ERSE outperforms existing rotation-equivariant estimators in reducing out-of-sample portfolio variance, achieving average risk reductions of 10.52\% versus linear shrinkage methods and 12.46\% versus nonlinear shrinkage methods. Further checks indicate that ERSE yields covariance matrices with lower condition numbers, produces more concentrated and stable portfolio weights, and provides consistent improvements across different subperiods and estimation windows. |
| Date: | 2025–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2507.01545 |
| By: | Qizhao Chen |
| Abstract: | This paper presents a dynamic cryptocurrency portfolio optimization strategy that integrates technical indicators and sentiment analysis to enhance investment decision-making. The proposed method employs the 14-day Relative Strength Index (RSI) and 14-day Simple Moving Average (SMA) to capture market momentum, while sentiment scores are extracted from news articles using the VADER (Valence Aware Dictionary and sEntiment Reasoner) model, with compound scores quantifying overall market tone. The large language model Google Gemini is used to further verify the sentiment scores predicted by VADER and give investment decisions. These technical indicator and sentiment signals are incorporated into the expected return estimates before applying mean-variance optimization with constraints on asset weights. The strategy is evaluated through a rolling-window backtest over cryptocurrency market data, with Bitcoin (BTC) and an equal-weighted portfolio of selected cryptocurrencies serving as benchmarks. Experimental results show that the proposed approach achieves a cumulative return of 38.72, substantially exceeding Bitcoin's 8.85 and the equal-weighted portfolio's 21.65 over the same period, and delivers a higher Sharpe ratio (1.1093 vs. 0.8853 and 1.0194, respectively). However, the strategy exhibits a larger maximum drawdown (-18.52%) compared to Bitcoin (-4.48%) and the equal-weighted portfolio (-11.02%), indicating higher short-term downside risk. These results highlight the potential of combining sentiment and technical signals to improve cryptocurrency portfolio performance, while also emphasizing the need to address risk exposure in volatile markets. |
| Date: | 2025–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2508.16378 |
| By: | Teemu Pennanen; Waleed Taoum |
| Abstract: | SOFR derivatives market remains illiquid and incomplete so it is not amenable to classical risk-neutral term structure models which are based on the assumption of perfect liquidity and completeness. This paper develops a statistical SOFR term structure model that is well-suited for risk management and derivatives pricing within the incomplete markets paradigm. The model incorporates relevant macroeconomic factors that drive central bank policy rates which, in turn, cause jumps often observed in the SOFR rates. The model is easy to calibrate to historical data, current market quotes, and the user's views concerning the future development of the relevant macroeconomic factors. The model is well suited for large-scale simulations often required in risk management, portfolio optimization and indifference pricing of interest rate derivatives. |
| Date: | 2025–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2508.02691 |
| By: | Diego Vallarino |
| Abstract: | This study develops and empirically validates a Mixture of Experts (MoE) framework for stock price prediction across heterogeneous volatility regimes using real market data. The proposed model combines a Recurrent Neural Network (RNN) optimized for high-volatility stocks with a linear regression model tailored to stable equities. A volatility-aware gating mechanism dynamically weights the contributions of each expert based on asset classification. Using a dataset of 30 publicly traded U.S. stocks spanning diverse sectors, the MoE approach consistently outperforms both standalone models. Specifically, it achieves up to 33% improvement in MSE for volatile assets and 28% for stable assets relative to their respective baselines. Stratified evaluation across volatility classes demonstrates the model's ability to adapt complexity to underlying market dynamics. These results confirm that no single model suffices across market regimes and highlight the advantage of adaptive architectures in financial prediction. Future work should explore real-time gate learning, dynamic volatility segmentation, and applications to portfolio optimization. |
| Date: | 2025–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2508.02686 |
| By: | Dimitrios Emmanoulopoulos; Ollie Olby; Justin Lyon; Namid R. Stillman |
| Abstract: | Large language models (LLMs) are increasingly deployed in agentic frameworks, in which prompts trigger complex tool-based analysis in pursuit of a goal. While these frameworks have shown promise across multiple domains including in finance, they typically lack a principled model-building step, relying instead on sentiment- or trend-based analysis. We address this gap by developing an agentic system that uses LLMs to iteratively discover stochastic differential equations for financial time series. These models generate risk metrics which inform daily trading decisions. We evaluate our system in both traditional backtests and using a market simulator, which introduces synthetic but causally plausible price paths and news events. We find that model-informed trading strategies outperform standard LLM-based agents, improving Sharpe ratios across multiple equities. Our results show that combining LLMs with agentic model discovery enhances market risk estimation and enables more profitable trading decisions. |
| Date: | 2025–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2507.08584 |
| By: | Roshan Shah |
| Abstract: | We introduce a modular framework that extends the signature method to handle American option pricing under evolving volatility roughness. Building on the signature-pricing framework of Bayer et al. (2025), we add three practical innovations. First, we train a gradient-boosted ensemble to estimate the time-varying Hurst parameter H(t) from rolling windows of recent volatility data. Second, we feed these forecasts into a regime switch that chooses either a rough Bergomi or a calibrated Heston simulator, depending on the predicted roughness. Third, we accelerate signature-kernel evaluations with Random Fourier Features (RFF), cutting computational cost while preserving accuracy. Empirical tests on S&P 500 equity-index options reveal that the assumption of persistent roughness is frequently violated, particularly during stable market regimes when H(t) approaches or exceeds 0.5. The proposed hybrid framework provides a flexible structure that adapts to changing volatility roughness, improving performance over fixed-roughness baselines and reducing duality gaps in some regimes. By integrating a dynamic Hurst parameter estimation pipeline with efficient kernel approximations, we propose to enable tractable, real-time pricing of American options in dynamic volatility environments. |
| Date: | 2025–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2508.07151 |
| By: | Drew M. Thomas |
| Abstract: | What grounds the rule of thumb that a(n American) retiree can safely withdraw 4% of their initial retirement wealth in their first year of retirement, then increase that rate of consumption with inflation? I investigate that question with a discrete-time model of returns to a retirement portfolio consumed at a rate that grows by $s$ per period. The model hinges on the parameter $\gamma$, an $s$-adjusted rate of return to wealth, derived from the first 2-4 moments of the portfolio's probability distribution of returns; for a retirement lasting $t$ periods the model recommends a rate of consumption of $\gamma / (1 - (1 - \gamma)^t)$. Estimation of $\gamma$ (and hence of the implied rate of spending down in retirement) reveals that the 4% rule emerges from adjusting high expected rates of return down for: consumption growth, the variance in (and kurtosis of) returns to wealth, the longevity risk of a retiree potentially underestimating $t$, and the inclusion of bonds in retirement portfolios without leverage. The model supports leverage of retirement portfolios dominated by the S&P 500, with leverage ratios $> 1.6$ having been historically optimal under the model's approximations. Historical simulations of 30-year retirements suggest that the model proposes withdrawal rates having roughly even odds of success, that leverage greatly improves those odds for stocks-heavy portfolios, and that investing on margin could have allowed safe withdrawal rates $> 6$% per year. |
| Date: | 2025–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2508.10273 |
| By: | Jingtang Ma; Xianglin Wu; Wenyuan Li |
| Abstract: | This paper studies the pricing problem in which the underlying asset follows a non-Markovian stochastic volatility model. Classical partial differential equation methods face significant challenges in this context, as the option prices depend not only on the current state, but also on the entire historical path of the process. To overcome these difficulties, we reformulate the asset dynamics as a rough stochastic differential equation and then represent the rough paths via linear or non-linear combinations of time-extended Brownian motion signatures. This representation transforms a rough stochastic differential equation to a classical stochastic differential equation, allowing the application of standard analytical tools. We propose a deep signature approach for both linear and nonlinear representations and rigorously prove the convergence of the algorithm. Numerical examples demonstrate the effectiveness of our approach for both Markovian and non-Markovian volatility models, offering a theoretically grounded and computationally efficient framework for option pricing. |
| Date: | 2025–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2508.15237 |
| By: | Ivan Letteri |
| Abstract: | The detection of outliers within cryptocurrency limit order books (LOBs) is of paramount importance for comprehending market dynamics, particularly in highly volatile and nascent regulatory environments. This study conducts a comprehensive comparative analysis of robust statistical methods and advanced machine learning techniques for real-time anomaly identification in cryptocurrency LOBs. Within a unified testing environment, named AITA Order Book Signal (AITA-OBS), we evaluate the efficacy of thirteen diverse models to identify which approaches are most suitable for detecting potentially manipulative trading behaviours. An empirical evaluation, conducted via backtesting on a dataset of 26, 204 records from a major exchange, demonstrates that the top-performing model, Empirical Covariance (EC), achieves a 6.70% gain, significantly outperforming a standard Buy-and-Hold benchmark. These findings underscore the effectiveness of outlier-driven strategies and provide insights into the trade-offs between model complexity, trade frequency, and performance. This study contributes to the growing corpus of research on cryptocurrency market microstructure by furnishing a rigorous benchmark of anomaly detection models and highlighting their potential for augmenting algorithmic trading and risk management. |
| Date: | 2025–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2507.14960 |