Are Financial Phenomena Random? On the Limits of the Probabilistic Description of Risk
This paper asks whether the fundamental assumption underlying financial risk management — the random character of financial phenomena — is justified. Its point of reference is hydrology, a discipline in which the same conceptual apparatus (the return period, the T-year event, the assumptions of stationarity and independence) was developed over a hundred years ago, and which has since declared a crisis in these very foundations. The paper traces how the probabilistic view of the world — from the random walk, through the normal distribution, to Value at Risk and Basel II's internal models — made its way into finance, alongside the philosophical lineage of instrumentalism that shielded these models' assumptions from scrutiny. It also examines the financial safety architecture in light of successive crises — including 2008 and the 2023 episode — which have struck more often than its own conservative parameters would suggest. The paper then formulates a catalog of considerations that call into question the validity of applying classical statistical description to socio-economic phenomena: their endogenous, speculative, and cumulative character; the intersubjective rather than objective nature of the modeled value; the questionable stationarity of socio-economic processes; and the absence of any real distinction between the expected world and the world of extreme events. Rather than calling for the abandonment of statistical methods in finance, the paper argues that they ought to play a complementary, rather than central, role, relative to a deeper understanding of the mechanics actually governing the financial sector.
I Can't Predict a 1,000-Year Catastrophe
Under the Basel regulations, the 0.999 quantile — the central parameter of the financial safety architecture, on which capital requirements for credit, operational, and numerous Pillar II risks have long been based — is interpreted in supervisory documents as an event occurring "once in a thousand years." Rather than revisiting the well-established critique of estimation difficulties at distant quantiles, this paper asks whether the temporal interpretation itself has any statistical, regulatory, or practical justification. It traces how this interpretation was embedded across successive Basel accords and disseminated in academic work, and demonstrates that it derives from a borrowed, never explicitly acknowledged, hydrological concept — the return period, used to describe phenomena such as the hundred-year flood. Transferring this convention to socio-economic phenomena, the paper shows, requires a tacit assumption about indexing risk realizations along a time axis — one lacking the natural justification it has in physical phenomena. The 1,000-year event, moreover, is neither embedded in risk model construction nor verifiable through backtesting, and is rendered redundant by regular model recalibration. Drawing on hydrology's own revision of its analogous "hundred-year flood" concept, the paper argues for a similar debate in finance, and concludes that the temporal interpretation of the 0.999 quantile is an empty artifact — one that should be replaced with definitions grounded in the actual mechanics of extreme events.
Why Do "100-Years Crisis" Happen Every 10 Years
A lecture delivered at several Polish universities, combining hydrology, statistics, philosophy of science, and financial history to explain why the concept of a "once in 100/1000 years" event — the very foundation of banking regulation (Basel I/II, VaR, AAA ratings) — failed in practice during the 2008 financial crisis. The starting point is the concept of the return period, rooted in hydrology (Fuller, Hazen, extreme value theory), and the question of whether it can safely be transferred to socio-economic phenomena. The lecture traces the history of thinking about randomness — from the deterministic world of Newton and Laplace, through the Maxwell-Boltzmann breakthrough, Bachelier's random walk theory of prices, to Markowitz, Fama, Black-Scholes, and David Li's Gaussian copula, which became the foundation for pricing CDOs and CDS. The second part examines the mechanics of the 2008 crisis (securitization, regulatory arbitrage, the role of AIG and rating agencies) and the six model assumptions that turned out to be false. The lecture closes with a philosophical reflection — drawing on Knight, Minsky, Hayek, and Taleb — on the distinction between risk and uncertainty, and on why statistical models themselves become a source of the systemic risk they claim to measure.
The AMA Method - Analytical Foundations of Its Failure
As of January 1, 2025, after twenty years in operation, the Advanced Measurement Approach (AMA) for operational risk was withdrawn, largely due to a "loss of confidence" stemming from high result volatility and significant capital discrepancies among banks with similar risk profiles. This paper shows that AMA's failure stemmed not from bank-level implementation, but from the framework's own construction: combining the actuarial frequency-severity approach with mandatory heavy-tailed distributions produces three unavoidable effects — (1) at distant quantiles, the annual loss aggregate is dominated by a single extreme loss (often exceeding 90%); (2) this loss sits at a single-loss quantile (0.9999+) far beyond what modeling methods can reliably estimate, given the required aggregate quantile of 0.999; and (3) the extreme loss's value can depend nonsensically on the number of minor events, contradicting business logic. Confirmed through simulation across a wide range of distributions, these findings warn against similar errors in future regulatory standards: overcomplexity and poorly defined core concepts lead to systemic failure.
Post-Crisis Financial Security Architecture in the Face of the 2023 Crisis Episode
This article examines the 2023 US regional bank failures to assess the post-2008 financial safety architecture's effectiveness. Reconstructing events through a review of the literature and regulatory documents, it finds that the banks involved met their capital—and often liquidity—requirements; the real causes were qualitative: poor risk management, unsustainable business models, and inadequate supervision. The episode also revealed a new crisis mechanics, as social media and digital banking compressed deposit runs from days to hours, fundamentally altering tail-risk dynamics. The article concludes that the existing regulatory framework, built on the paradigm of normally distributed phenomena and quantitative risk measures, is ill-suited to this new reality—distribution tails are fatter, and future crises may prove more violent and harder to contain. Though limited in scale, the 2023 episode should be treated as a warning sign for the financial safety system as a whole.
Bieg wsteczny w koncepcji modelowania wartości nieoczekiwanej w sektorze finansowym na przykładzie decyzji o wycofaniu frameworku AMA w ryzyku operacyjnym
1 stycznia 2025 r. za pośrednictwem przepisów CRR III weszła w życie nowa architektura bezpieczeństwa sektora finansowego. Działaniom związanym z wypracowaniem nowych regulacji towarzyszyła pogłębiona refleksja na temat skuteczności dotychczasowej, opracowanej w 2004 r. (Basel II) koncepcji bezpieczeństwa kapitałowego. W niektórych obszarach refleksja ta zaprowadziła regulatora do decyzji dychotomicznych i ostatecznych. Taką decyzję podjęto w stosunku do stosowanej w przestrzeni ryzyka operacyjnego Metody Zaawansowanego Pomiaru AMA. W niniejszym artykule staram się przedstawić szeroki kontekst, jaki tej decyzji towarzyszył, wraz z własnym osądem sytuacji.
Badanie autoregresyjnego charakteru procesu liczby strat operacyjnych
Artykuł przedstawia sposób wykorzystania modeli autoregresyjnych w odniesieniu do liczby strat operacyjnych w ramach modelowania ryzyka operacyjnego. Przedstawiono liczbę strat operacyjnych jako proces stochastyczny. Następnie przeprowadzono badanie wewnętrznej struktury zdefiniowanego procesu. W szczególności przedmiot badania stanowiła identyfikacja autoregresyjnego charakteru procesu liczby strat operacyjnych.