Risks

21 pages, 2420 KB

Open AccessArticle

Does Carbon Pricing Displace Crypto-Mining Emissions? Quantile Evidence on Carbon Leakage from EU27, Russian and Rest-of-World Power Grids

by Pham Ngoc Toan, Le Tran Trung Hieu and Nguyen Vu Trung Nguyen

Risks 2026, 14(8), 187; https://doi.org/10.3390/risks14080187 - 21 Aug 2026

Viewed by 355

Abstract

Carbon pricing is jurisdictional, while proof-of-work cryptocurrency mining is a highly mobile electricity load. We examine whether daily power-sector emissions display a cross-regional and distributional pattern consistent with short-run emissions displacement. Using daily observations covering calendar years 2019–2025 (with a boundary observation on [...] Read more.

Carbon pricing is jurisdictional, while proof-of-work cryptocurrency mining is a highly mobile electricity load. We examine whether daily power-sector emissions display a cross-regional and distributional pattern consistent with short-run emissions displacement. Using daily observations covering calendar years 2019–2025 (with a boundary observation on 1 January 2026; N = 2550 after transformation and cleaning), we estimate quantile regressions for the EU27, the Russian Federation and the rest of the world using the interaction between Bitcoin returns and European carbon-allowance returns. The focal Russian lower-tail interaction is positive (q10 beta = 0.0662); OLS and dynamic specifications remain positive, and a 1000-replication pairs bootstrap gives p = 0.0077. The association survives a trading-day-only sample, calendar and persistence controls, and a seven-lag specification, while randomised-carbon and non-power-sector placebo outcomes are null. However, the coefficient loses conventional significance without Winsorisation, the May-2021 Chinese-ban timing prediction is not supported, and a direct EU27-minus-Russia substitution diagnostic is null. Quantile-on-quantile estimates place the largest Russian Bitcoin-return coefficients in high-carbon-price, low-emission states, but remain descriptive. Because the design does not observe mining capacity moving across jurisdictions and the available full-sample Russian emissions series is national rather than subnational, the evidence supports a leakage-consistent operational association rather than proof of physical relocation or a broad causal effect of EU carbon pricing. Full article

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29 pages, 1514 KB

Open AccessArticle

Analysis of the Mitigating Effect of Financial Regulatory Penalties on Bank Systemic Risk

by Wenlong Miao, Siyu Zhang and Yuanyuan Huo

Risks 2026, 14(8), 186; https://doi.org/10.3390/risks14080186 - 20 Aug 2026

Viewed by 240

Abstract

Financial regulatory penalties are a critical tool for curbing bank violations and play an important role in safeguarding the banking system against systemic risk. This study examines the effects of regulatory penalties imposed by the People’s Bank of China (PBOC) and the National [...] Read more.

Financial regulatory penalties are a critical tool for curbing bank violations and play an important role in safeguarding the banking system against systemic risk. This study examines the effects of regulatory penalties imposed by the People’s Bank of China (PBOC) and the National Financial Regulatory Administration (NFRA) on bank systemic risk. We construct a unique dataset of 10,462 penalty decisions manually collected from 2014 to 2023, and employ a two-way fixed effects model to identify the impact of regulatory penalties. The results show that financial regulatory penalties exert a significant mitigating effect on bank systemic risk. This effect operates through two primary channels: first, by reducing the idiosyncratic risk of individual banks; and second, by weakening the intensity of risk transmission across institutions. The risk-controlling effect is further amplified under higher regulatory pressure and stronger creditor oversight. Heterogeneity analysis reveals that the penalty effect varies by penalty type, bank level, and regulatory authority, and is more pronounced for monetary fines, penalties imposed on provincial and municipal branches, and enforcement actions conducted by the NFRA. Notably, when banking institutions and the broader banking system are already in an extreme risk state, financial regulatory penalties may cease to serve as an effective tool for containing systemic risk and preserving financial stability. Our findings suggest that strengthening the enforcement and coordination of macroprudential and microprudential supervision, along with reinforcing market discipline, can enhance the effectiveness of financial penalties in safeguarding financial stability. Full article

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21 pages, 797 KB

Open AccessArticle

Gold Price Transmission and Tail Risk in a Frontier Commodity Market: Evidence from Vietnam

by Huong Thu Nguyen and Dung Quang Nguyen

Risks 2026, 14(8), 185; https://doi.org/10.3390/risks14080185 - 20 Aug 2026

Viewed by 818

Abstract

Vietnam’s domestic gold price has persistently exceeded the world price by a wide margin, even as recent reforms have begun to relax the state’s historical monopoly over gold-bar production and imports. This paper asks why the gap persists, and whether it is confined [...] Read more.

Vietnam’s domestic gold price has persistently exceeded the world price by a wide margin, even as recent reforms have begun to relax the state’s historical monopoly over gold-bar production and imports. This paper asks why the gap persists, and whether it is confined to normal market conditions or extends into periods of extreme price movement. Using daily data spanning 2 January 2019 to 31 July 2026 (1856 trading days), covering the reform introduced by Decree No. 232/2025/ND-CP we decompose the domestic premium into a currency component and a pure physical-gold component, and use a copula-based framework to separately assess average price linkage and tail (extreme-event) co-movement between the domestic and world markets. Domestic gold bars traded at an average premium of 16.0% over import-parity world prices, of which 13.8 percentage points reflect the physical-gold component driven by constrained arbitrage, while currency factors account for only about 2 percentage points. The average linkage between the two markets is weak, indicating persistent segmentation, and this segmentation extends into the tails of the distribution for most of the sample. The premium itself carries substantial latent risk: a reversion to price parity would imply a one-off loss of about 9.6% of value, roughly eight to ten times the historical one-day 5% Value-at-Risk. Following the reform’s effective date, however, we find early evidence of emerging co-movement specifically in extreme upside price movements, even though the physical premium itself has not yet narrowed—consistent with a reform that has been enacted in law but remains at an early stage of operational implementation. The results indicate that administrative restrictions on the physical gold supply chain, rather than currency controls, are the principal source of Vietnam’s persistent gold-price gap, with direct implications for how the ongoing liberalization process should be sequenced. Full article

(This article belongs to the Special Issue Fundamentals and Risk Factors in Commodity Markets)

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25 pages, 1402 KB

Open AccessArticle

Governing the Tradeoff Between Predictive Accuracy and Adversarial Robustness: An Enterprise Model Risk Framework

by Andrew Kumiega and Ruiqing Xu

Risks 2026, 14(8), 184; https://doi.org/10.3390/risks14080184 - 19 Aug 2026

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Abstract

Machine learning models used in financial decision systems create a measurable risk tradeoff between predictive performance and resilience to adversarial manipulation. This study presents a governance framework for managing that tradeoff through stepwise adversarial hardening guided by feature importance. It introduces three enterprise [...] Read more.

Machine learning models used in financial decision systems create a measurable risk tradeoff between predictive performance and resilience to adversarial manipulation. This study presents a governance framework for managing that tradeoff through stepwise adversarial hardening guided by feature importance. It introduces three enterprise risk measures—Management Attack Success Risk (MASR), Robustness Overfitting Risk (ROR), and the Robustness Accuracy Exchange Score (RAES)—that quantify residual adversarial risk and the business cost of robustness controls. The proposed measures provide decision-oriented evidence for risk governance, risk acceptance, and control oversight. Full article

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26 pages, 499 KB

Open AccessArticle

The Effect of Digital Washing on Firm Value: The Mediating Role of ESG Performance

by Anh Tuan Dao, Pham Bao Ngoc Le, Nguyen Thanh An Thieu, Hai Anh Le, Trinh Thu Huong Tran and Huong Giang To

Risks 2026, 14(8), 183; https://doi.org/10.3390/risks14080183 - 19 Aug 2026

Viewed by 265

Abstract

Digital transformation has become a strategic pillar for firms; however, it requires substantial time, resources, and investment. These challenges have led to the emergence of an alternative phenomenon, digital washing. Using 2527 samples spanning six years, this study investigates the effect of digital [...] Read more.

Digital transformation has become a strategic pillar for firms; however, it requires substantial time, resources, and investment. These challenges have led to the emergence of an alternative phenomenon, digital washing. Using 2527 samples spanning six years, this study investigates the effect of digital washing on firm value and examines whether ESG performance mediates this relationship in the context of ASEAN-4, which includes Malaysia, Indonesia, the Philippines, and Thailand, together with Vietnam. Path analysis and bootstrapping were conducted. The research results indicate that digital washing positively affects firm value, yet ESG performance does not play a statistically significant mediating role. These findings enrich the literature by clarifying the effects of digital washing; moreover, they provide updated empirical evidence from the ASEAN-4 and Vietnam, where research on digital washing remains scarce. Full article

11 pages, 437 KB

Open AccessArticle

Contagion of Affinity: Predicting CDS Spikes in Global Systemically Important Banks

by Gisela Reichmuth

Risks 2026, 14(8), 182; https://doi.org/10.3390/risks14080182 - 14 Aug 2026

Viewed by 402

Abstract

This paper examines the predictive power of credit default swap (CDS) spread correlations in the context of the 2023 Credit Suisse failure. Using a two-window design, we separate a 50-week pre-crisis period from the final two-week “jump” window and evaluate whether historical market-implied [...] Read more.

This paper examines the predictive power of credit default swap (CDS) spread correlations in the context of the 2023 Credit Suisse failure. Using a two-window design, we separate a 50-week pre-crisis period from the final two-week “jump” window and evaluate whether historical market-implied dependence anticipated cross-sectional crisis repricing across Global Systemically Important Banks (G-SIBs). We find that the magnitude of each bank’s crisis-period CDS jump is significantly related to its prior co-movement with Credit Suisse across the full sample (

r = 0.80

,

p < 0.001

,

n = 15

), indicating that contagion followed a structured dependence pattern rather than an undifferentiated panic dynamic. The relationship holds across both regional cohorts, with the European G-SIB group displaying a considerably tighter fit (

r = 0.96

,

p < 0.001

,

n = 8

) than the non-European group (

r = 0.84

,

p = 0.019

,

n = 7

), consistent with geographic and institutional proximity to Credit Suisse amplifying the contagion channel. Additional empirical outputs, including stepwise-regression diagnostics and placebo/event-time checks, support the interpretation that the estimated relationship contains an economically meaningful signal while remaining partly event-driven in short horizons. Overall, the evidence suggests that rolling CDS dependence regimes may serve as a useful leading indicator for identifying institutions most likely to face disproportionate repricing pressure during a localized systemic shock. These findings are drawn from a single crisis episode and 15 peer institutions; they should be read as preliminary evidence of a potentially useful mechanism rather than as the basis for an operational early-warning system, and replication across additional crises and institutional settings is required before broader generalization. Full article

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21 pages, 1858 KB

Open AccessArticle

Exchange-Rate Volatility and Financial Stability in the Banking Sector: Distributional Evidence from G7 and High-Income European Economies

by Ivana Miklošević, Katerina Fotova Čiković and Anica Vukašinović

Risks 2026, 14(8), 181; https://doi.org/10.3390/risks14080181 - 13 Aug 2026

Viewed by 297

Abstract

The present study examined how volatility in exchange rates shapes banking-sector financial stability across the G7 and six high-income European countries, consisting of 13 developed economies. The study analyses the time period from 2000 to 2023. To measure volatility, the present study employed [...] Read more.

The present study examined how volatility in exchange rates shapes banking-sector financial stability across the G7 and six high-income European countries, consisting of 13 developed economies. The study analyses the time period from 2000 to 2023. To measure volatility, the present study employed the GARCH(1,1) conditional variance of monthly real effective exchange rates. Stability is measured through the following two supporting indicators: Bank Z-score (solvency) and Non-Performing Loan (NPL) ratio (credit quality). Our analysis combines the Fully Modified OLS and two-step System GMM for analysing long-run and dynamic effects. To assess distributional heterogeneity, Method of Moments Quantile Regression (MMQR) is employed, while Dumitrescu–Hurlin tests are used for examining causality. The results show that volatility in exchange rates significantly reduces bank solvency and elevates credit risk. These effects are highly uneven: the adverse impact falls on the most fragile banking systems—those in the lower quantiles of the Z-score distribution and the upper quantiles of the NPL distribution. Causality runs unidirectionally, moving from volatility to instability. Institutional quality, which is proxied by the rule of law and regulatory quality, is seen to significantly decrease the credit-risk channel but not the solvency channel. Our findings provide implications for developed economies and support targeted, fragility-sensitive macro-prudential policy. Full article

(This article belongs to the Topic The Future of Banking and Financial Risk Management)

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18 pages, 537 KB

Open AccessArticle

Evaluating Risk and Performance in Non-Life Insurance Markets: Evidence from EU and EEA Countries

by Neylan Kaya, Güler Ferhan Ünal Uyar, Aslıhan Ersoy Bozcuk, Mustafa Terzioğlu, Burçin Tutcu and Hasan Talaş

Risks 2026, 14(8), 180; https://doi.org/10.3390/risks14080180 - 12 Aug 2026

Viewed by 334

Abstract

Non-life insurance markets face growing pressure from inflation, geopolitical uncertainty, and climate-related risks. These developments increase the need for comprehensive performance evaluation from a risk-based perspective. In this context, this study examines the risk-based performance of non-life insurance markets across European Union (EU) [...] Read more.

Non-life insurance markets face growing pressure from inflation, geopolitical uncertainty, and climate-related risks. These developments increase the need for comprehensive performance evaluation from a risk-based perspective. In this context, this study examines the risk-based performance of non-life insurance markets across European Union (EU) and European Economic Area (EEA) countries using an integrated multi-criteria decision-making (MCDM) framework. The analysis includes eight indicators related to profitability, liquidity, growth, capital adequacy, and risk. Criterion weights were calculated using the Modified Standard Deviation (MSD) and Modified Preference Selection Index (MPSI) methods. These weights were then combined to obtain a single objective weighting structure. Subsequently, country rankings were obtained through the Combined Compromise Solution (CoCoSo) method. The data were taken from the European Insurance and Occupational Pensions Authority (EIOPA) database. The findings show that ROE and ROA received the highest integrated objective weights and contributed most strongly to differentiating country performance within the analyzed dataset. Austria, Germany, and Cyprus ranked as the highest-performing countries. The sensitivity analysis under different λ values also shows that the ranking results are stable. The results suggest that non-life insurance performance should not be evaluated only through profitability. Solvency strength, liquidity capacity, and risk exposure should also be considered. The study provides an integrated framework for comparative country-level assessment of non-life insurance markets and offers useful insights for regulators and policymakers. Full article

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23 pages, 436 KB

Open AccessArticle

Bankruptcy Prediction from 10-K Narratives: Evidence from Interpretable Text Scores and Accounting Baselines

by Zhen Zhang, Moxuan Zheng, Tongchen Zhang, Luyun Lin and Lixing Lin

Risks 2026, 14(8), 179; https://doi.org/10.3390/risks14080179 - 10 Aug 2026

Viewed by 428

Abstract

This study examines whether context-validated acute distress disclosures in annual Form 10-K filings improve bankruptcy-risk ranking beyond accounting variables. The analysis links U.S. Securities and Exchange Commission filing data, Item 7 Management’s Discussion and Analysis text, and bankruptcy events from the Florida–UCLA–LoPucki Bankruptcy [...] Read more.

This study examines whether context-validated acute distress disclosures in annual Form 10-K filings improve bankruptcy-risk ranking beyond accounting variables. The analysis links U.S. Securities and Exchange Commission filing data, Item 7 Management’s Discussion and Analysis text, and bankruptcy events from the Florida–UCLA–LoPucki Bankruptcy Research Database for fiscal years 2010–2021. The primary sample contains 21,239 nonfinancial firm-year observations and 159 one-year bankruptcy events. The paper develops a Validated Distress Disclosure (VDD) Dictionary that flags going-concern uncertainty, covenant noncompliance, and lender forbearance or waiver after sentence-level context filtering. In the 2019–2021 holdout test, adding VDD indicators to a six-variable Ohlson-related accounting baseline increases the area under the receiver operating characteristic curve (AUC) from 0.8682 to 0.8827 (

Δ = 0.0146

; 95% confidence interval (CI) [0.0040, 0.0275]) and precision–recall AUC (PR-AUC) from 0.0924 to 0.2060 (

Δ = 0.1136

; 95% CI [0.0458, 0.2132]). Benchmark and decomposition tests indicate that the main signal is concentrated in going-concern disclosures and that VDD is best interpreted as an auditable ranking supplement to accounting variables and broader text models, not as a calibrated probability-of-default model. Full article

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39 pages, 26410 KB

Open AccessFeature PaperArticle

When Should Demographics Enter the Prior? Conditional Exchangeability in Bayesian Estimation of Risk Preferences

by Xiaoxue Sherry Gao and Glenn W. Harrison

Risks 2026, 14(8), 178; https://doi.org/10.3390/risks14080178 - 4 Aug 2026

Viewed by 303

Abstract

Hierarchical Bayesian models for the estimation of individual risk preferences typically assume that subjects are unconditionally exchangeable: prior to seeing any data, every subject is treated as a draw from a common population distribution. We examine the consequences of relaxing that assumption to [...] Read more.

Hierarchical Bayesian models for the estimation of individual risk preferences typically assume that subjects are unconditionally exchangeable: prior to seeing any data, every subject is treated as a draw from a common population distribution. We examine the consequences of relaxing that assumption to one of conditional exchangeability, where the hyper-parameters of the population distribution are allowed to depend on observable covariates. Using simulated data, where the true parameters are known, we compare the recovery properties of unconditionally and conditionally exchangeable specifications across both Expected Utility and Rank-Dependent Utility models. A parsimonious conditionally exchangeable specification recovers individual risk preferences well when the data-generating process actually contains demographic structure, and imposes only a modest penalty when it does not, but overly rich covariate specifications can substantially erode the borrowing-of-strength that makes hierarchical models attractive in the first place. The trade-off is sharp, but navigable, and is of direct relevance to applied work that uses estimated risk preferences as inputs to normative welfare analysis or as controls for other inferences. Full article

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22 pages, 1144 KB

Open AccessArticle

Narrative Disclosure and Private Credit Risk: Text-Based Evidence from BDC Filings Amid Macro-Financial Shocks

by Colin Ellis

Risks 2026, 14(8), 177; https://doi.org/10.3390/risks14080177 - 3 Aug 2026

Viewed by 397

Abstract

A persistent difficulty in monitoring private-credit risk is that narrative and quantitative information in periodic filings are produced jointly but evaluated separately. This leaves open the question of whether disclosure language is a useful signal of risk management behaviour or merely an echo [...] Read more.

A persistent difficulty in monitoring private-credit risk is that narrative and quantitative information in periodic filings are produced jointly but evaluated separately. This leaves open the question of whether disclosure language is a useful signal of risk management behaviour or merely an echo of conditions already visible in published data. For business development companies (BDCs), this separation carries a particular cost: the sector sits at the intersection of private credit, fair-value accounting, and floating-rate funding, where filing language about portfolio conditions and the macro environment may reflect the cycle itself rather than add to what published rate and spread data already reveal. This paper asks two questions. First, do aggregate BDC text measures of macro and portfolio-credit language co-move with key macro series over time? Second, does cross-sectional text intensity relate in a stable, linear way to the same BDC’s reported ratios and their volatility? Using dictionary-based filing scores linked to over 590 BDC observations and macro series from 2010 to 2025, we find macro text in filings correlates strongly with variables such as the Federal funds rate and the two-year Treasury yield. Portfolio-credit text lines up with corporate spreads and the unemployment rate. At the firm-year level, associations between text and balance-sheet outcomes are weak. This indicates that BDC narratives are linked with the macro cycle, but there is not a tight mapping to risk metrics in reported financials from year to year, consistent with a degree of insulation in private credit from prevailing macro conditions. For creditors, investors, and supervisors of private-credit vehicles, this asymmetry of macro co-movement without firm-level signal has direct implications for how narrative disclosure should be weighted in risk monitoring and governance frameworks. The aggregate regression results are based on sixteen annual observations and should be interpreted accordingly. Full article

(This article belongs to the Special Issue Empirical Advances in Corporate Finance and Governance Under Emerging Risks and Strategic Challenges)

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24 pages, 2262 KB

Open AccessArticle

Measurement Sensitivity of the Determinants of Financial Flexibility Among JSE-Listed Non-Financial Firms

by Joseph Kayiira, Vusani Moyo and Freddy Munzhelele

Risks 2026, 14(8), 176; https://doi.org/10.3390/risks14080176 - 30 Jul 2026

Viewed by 458

Abstract

This study examines the sensitivity of empirical findings in financial flexibility research to alternative measurement approaches. Financial flexibility is widely recognised as a critical determinant of corporate financing and investment decisions, yet there is no consensus on its operational definition. Existing studies employ [...] Read more.

This study examines the sensitivity of empirical findings in financial flexibility research to alternative measurement approaches. Financial flexibility is widely recognised as a critical determinant of corporate financing and investment decisions, yet there is no consensus on its operational definition. Existing studies employ different proxies, including spare debt capacity, cash holdings, leverage positioning, and composite measures, which may capture distinct dimensions of financial flexibility. Using panel data from 106 non-financial firms listed on the JSE over the period 2000–2019, this study compares two widely used proxies: spare debt capacity derived from predicted leverage models and a composite low-leverage–high-cash measure. Fixed- and random-effects models, along with logistic regression, are employed to assess whether the determinants of financial flexibility remain consistent across these measures. The findings reveal substantial variation in coefficient signs, statistical significance, and economic interpretation across proxies. Classification-overlap analysis based on the common SDC–LLHC sample shows limited agreement between the proxies, with only 17.4% of common-sample firm-year observations classified as flexible under both measures and Cohen’s kappa indicating only slight agreement. Growth opportunities, retained earnings, dividend payout, and selected firm-specific variables exhibit strong sensitivity to measurement choice, while some relationships remain relatively stable. The results demonstrate that financial flexibility, as operationalised through alternative empirical proxies, is not measurement-neutral, and that proxy selection can materially alter empirical and theoretical conclusions. The study contributes to corporate finance literature by highlighting the importance of construct validity, proxy transparency, and robustness testing, particularly in emerging market contexts. Full article

(This article belongs to the Special Issue Financial Markets, Risk Modelling and Econometrics)

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22 pages, 1355 KB

Open AccessArticle

Application of Lean Management Principles in Risk Management

by Zuzanna Zaporowska and Marek Szczepański

Risks 2026, 14(8), 175; https://doi.org/10.3390/risks14080175 - 30 Jul 2026

Viewed by 797

Abstract

This study examines the impact of lean management principles on operational risk management in Polish Shared Service Centers (SSCs). Despite the increasing adoption of lean methodologies, their role in risk mitigation remains underexplored, particularly in service-based organizations. Using a mixed-methods approach, from September [...] Read more.

This study examines the impact of lean management principles on operational risk management in Polish Shared Service Centers (SSCs). Despite the increasing adoption of lean methodologies, their role in risk mitigation remains underexplored, particularly in service-based organizations. Using a mixed-methods approach, from September to October 2023, we conducted a diagnostic survey of 70 SSCs with established risk management functions and applied statistical analysis to assess the relationship between lean management and operational risk factors. The findings suggest that the implementation of lean principles is associated with measurable improvements, including a reduction in internal controls, fewer errors, lower fraud-related losses, and decreased system inefficiencies. The inferential results indicate that these relationships are not consistently dependent on the duration of lean management implementation. This study contributes to the lean risk management literature by demonstrating how lean methodologies enhance risk mitigation in service operations. The results provide actionable insights for managers seeking to optimize process efficiency while maintaining robust risk controls. Full article

(This article belongs to the Special Issue Risks in Corporate Finance)

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12 pages, 381 KB

Open AccessArticle

A Functional-Analytic Framework for Sensitivity Analysis in Actuarial Valuation

by Emmanuel Van Yeboah

Risks 2026, 14(8), 174; https://doi.org/10.3390/risks14080174 - 24 Jul 2026

Viewed by 360

Abstract

Actuarial valuation of long-duration insurance liabilities depends on assumptions regarding mortality, lapse behavior, and discount rates, making it important to understand how valuation outcomes respond to changes in these assumptions. Existing approaches primarily rely on stress testing, scenario analysis, and numerical sensitivity analysis, [...] Read more.

Actuarial valuation of long-duration insurance liabilities depends on assumptions regarding mortality, lapse behavior, and discount rates, making it important to understand how valuation outcomes respond to changes in these assumptions. Existing approaches primarily rely on stress testing, scenario analysis, and numerical sensitivity analysis, which provide limited theoretical insight into the stability and sensitivity of the valuation process. This paper formulates actuarial valuation as a nonlinear operator acting on a space of actuarial assumptions. We establish well-posedness, Lipschitz continuity, Fréchet differentiability, and second-order sensitivity expressions that characterize the response of valuation outcomes to simultaneous perturbations in mortality, lapse, and discount assumptions. The theoretical results are illustrated through a numerical example using mortality data from the Social Security Administration Actuarial Life Table, where the first- and second-order approximations closely match the exact perturbed valuations under the assumptions considered. The framework developed in this paper provides a new way to study how actuarial valuations respond to changes in mortality, lapse, and discount assumptions. Full article

30 pages, 8401 KB

Open AccessArticle

Bayesian Joint Estimation of the Hurst Parameter and Volatility with Applications to Fractional Option Pricing

by Hana H. Sagor, Edward L. Boone and Ryad A. Ghanam

Risks 2026, 14(8), 173; https://doi.org/10.3390/risks14080173 - 24 Jul 2026

Viewed by 514

Abstract

Fractional Brownian motion has been widely used in financial modeling to capture long-range dependence and persistent behavior in asset dynamics. In the fractional Black–Scholes framework, accurate estimation of the Hurst parameter is essential because estimation uncertainty can directly affect option pricing. In this [...] Read more.

Fractional Brownian motion has been widely used in financial modeling to capture long-range dependence and persistent behavior in asset dynamics. In the fractional Black–Scholes framework, accurate estimation of the Hurst parameter is essential because estimation uncertainty can directly affect option pricing. In this paper, we propose a Bayesian framework for joint inference on the Hurst parameter and volatility in fractional stochastic differential equation models. Unlike approaches based solely on point estimation, the proposed framework propagates posterior uncertainty directly into option pricing distributions under the fractional Black–Scholes model. Simulation studies are conducted across multiple values of the Hurst parameter and sample sizes to evaluate estimation accuracy, posterior coverage, and pricing uncertainty. The results demonstrate stable posterior inference and coherent uncertainty quantification for both model parameters and option prices. The methodology is further illustrated using WTI crude oil and natural gas data under different market regimes. The empirical analysis indicates that differences in market behavior are driven primarily by changes in volatility rather than strong long-range dependence, while posterior option price distributions exhibit substantial variation in pricing uncertainty across regimes. These findings highlight the importance of incorporating joint parameter uncertainty into fractional financial models and demonstrate the practical value of Bayesian methods for option pricing. Full article

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30 pages, 783 KB

Open AccessArticle

Bayesian Integrated Nested Laplace Approximation (INLA) Longevity Bonds Market Model

by Yethu Sithole and Samuel Asante Gyamerah

Risks 2026, 14(8), 172; https://doi.org/10.3390/risks14080172 - 24 Jul 2026

Viewed by 494

Abstract

Pricing coupon longevity bonds (CLBs) is challenging in illiquid markets due to the incompleteness of insurance markets and the unavailability of longevity payout data. In addition, pension funds may experience significant surges in annual mortality-improvement reserves (MIRs), consistent with systematic longevity drift and [...] Read more.

Pricing coupon longevity bonds (CLBs) is challenging in illiquid markets due to the incompleteness of insurance markets and the unavailability of longevity payout data. In addition, pension funds may experience significant surges in annual mortality-improvement reserves (MIRs), consistent with systematic longevity drift and cohort-survival effects. We propose a Bayesian pricing model based on the Integrated Nested Laplace Approximation (INLA) for CLBs in pension-fund applications. The term structure of interest rates is modeled using a two-factor Cox–Ingersoll–Ross (CIR) specification, while mortality dynamics are captured using a CIR affine jump–diffusion model to capture abrupt longevity shocks. Posterior inference is performed via INLA and benchmarked against Markov chain Monte Carlo (MCMC). Using South African government bond yield data, pension-fund MIR series, and population survival-rate reports, we show that INLA provides a computationally efficient approximation to the MCMC posterior with substantially reduced computation time. Longevity Greeks derived from the model support hedge construction and evaluation of strategies aimed at mitigating rising longevity-linked cash flows. Empirically, model-implied longevity payouts are positively skewed with high dispersion and exhibit frequent jump episodes over a broad range, underscoring the importance of jump risk in CLB valuation and hedging. Full article

(This article belongs to the Special Issue Innovations in Annuities and Longevity Risk Management)

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Risks, Volume 14, Issue 8 (August 2026) – 16 articles

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