Risks

Cryptocurrency markets combine persistent volatility, heavy tails, and recurrent stress episodes. This study asks whether portfolio optimization is sufficient to manage these risks for Bitcoin, Ethereum, Binance Coin, Solana, and XRP, using 1454 daily observations from January 2022 to January 2026. Student-t GARCH and DCC-GARCH forecasts feed static and rolling allocation rules, evaluated out of sample and net of transaction costs against equal-weight, minimum-variance, risk-parity, and minimum-CVaR benchmarks; downside risk is backtested with Kupiec and Christoffersen tests, and three anomaly detectors are validated against four crisis windows, including expanding-window refits. Volatility persistence ranges from 0.912 to 1.000, and average conditional correlations are higher inside four crisis windows than outside (0.76 vs. 0.66), a contrast that exceeds placebo windows but is small relative to neighbouring days. In sample, maximum-Sharpe weights raise the Sharpe ratio (0.88 vs. 0.76) without statistical significance; out of sample, their point estimate is lower than that of equal weighting (0.92 vs. 1.15), a difference that is statistically inconclusive. Risk-based rules cut volatility by about 19% and maximum drawdown by 10 points, whereas GARCH–DCC allocation adds turnover without further gains, and minimum-CVaR cannot be distinguished from minimum-variance allocation in this sample, the tests having limited power. Isolation Forest flags are about 8 times more concentrated in crisis windows than chance, and about 10 times when refitted on an expanding window. Optimization lowers risk, whereas evidence that it improves risk-adjusted performance is inconclusive.

In this paper, we consider applications of semi-Markov chains (SMCs) in bond and energy markets. The research work was conducted for semi-Markov-modulated exponential-affine bond prices, and for pricing and hedging European-style options under a semi-Markov-switching diffusion model. In the former case, we will focus on the Hull–White model and generalize the results to three states and more for the SMC. In the latter case, based on real data (daily Alberta electricity prices from 1 January 2020 to 31 December 2025, Alberta Electric System Operator (AESO)), it is observed that occupation time does not follow an exponential distribution for two out of four volatility states, which violates the Markov process conditions. Thus, we calculated call and put option prices for different maturities and strikes under the semi-Markov condition by applying the finite-difference method. We also calculate the option prices using the Markov-diffusion model, and the classical Black–Scholes (BS) call option price equation for comparison. The contributions of the paper are twofold: the application of SMCs with any number of states to bond pricing, and the applications of SMCs in energy markets with real market data.

This article explores the concept of systemic frailty as a structural condition, characterized by correlated vulnerabilities across financial institutions. Drawing on institutional theory, it examines how institutional isomorphism, regulatory incentives and legitimacy-seeking behavior may contribute to the emergence of such vulnerabilities within banking systems. European banks operate in an increasingly complex environment shaped by technological change, geopolitical tensions, evolving macroeconomic conditions and heightened societal expectations. While prudential regulation and supervision have materially strengthened capital adequacy, liquidity resilience, governance and risk-management practices, institutional and regulatory pressures may under certain conditions contribute to convergence in business models, risk perceptions and organizational behavior. Such convergence may increase the likelihood that common shocks affect multiple institutions simultaneously. Building on this insight, the article conceptualizes systemic frailty as a structural condition in which converging business models, risk perceptions, organizational practices and regulatory incentives generate correlated vulnerabilities across institutions. While correlation-driven vulnerabilities are well established in the systemic-risk literature, the contribution of the article lies in explaining how institutional isomorphism and regulatory incentives may contribute to their endogenous emergence. The article further distinguishes systemic frailty from related concepts such as contagion, common exposures, herding and systemic linkage. Using a conceptual and theory-building approach, the article develops a framework linking institutional isomorphism, innovation and systemic frailty. It concludes that supervisory frameworks may benefit from greater recognition of diversity, adaptability and correlated vulnerabilities alongside institution-level resilience. Finally, it proposes the Impact Factor as a conceptual supervisory overlay, designed to complement existing prudential frameworks by incorporating institutions’ contributions to system-wide diversity, adaptability and correlated vulnerability into supervisory assessments.