This study explores contagion in the Chinese stock market using Hawkes processes to analyze autocorrelation and cross-correlation in multivariate time series data. We examine whether market indices exhibit trending behavior and whether sector indices influence one another. By fitting self-exciting and inhibitory Hawkes processes to daily returns of indices like the Shanghai Composite, Shenzhen Component, and ChiNext, as well as sector indices (CSI Consumer, Healthcare, and Financial), we identify long- term dependencies and trending patterns, including upward, downward, and over- sold rebound trends. Results show that during high trading activity, sector indices tend to sustain their trends, while low activity periods exhibit strong sector rotation. This research models stock price movements using spatiotemporal Hawkes processes, leveraging conditional intensity functions to explain sector rotation, advancing the understanding of financial contagion.

This paper investigates the deep hedging framework, based on reinforcement learning (RL), for the dynamic hedging of swaptions, contrasting its performance with traditional sensitivity-based rho-hedging. We design agents under three distinct objective functions (mean squared error, downside risk, and Conditional Value-at-Risk) to capture alternative risk preferences and evaluate how these objectives shape hedging styles. Relying on a three-factor arbitrage-free dynamic Nelson-Siegel model for our simulation experiments, our findings show that near-optimal hedging effectiveness is achieved when using two swaps as hedging instruments. Deep hedging strategies dynamically adapt the hedging portfolio's exposure to risk factors across states of the market. In our experiments, their out-performance over rho-hedging strategies persists even in the presence some of model misspecification. These results highlight RL's potential to deliver more efficient and resilient swaption hedging strategies.

Autodeleveraging (ADL) is a last-resort loss socialization mechanism for perpetual futures venues. It is triggered when solvency-preserving liquidations fail. Despite the dominance of perpetual futures in the crypto derivatives market, with over \60 trillion of volume in 2024, there has been no formal study of ADL. In this paper, we provide the first rigorous model of ADL. We prove that ADL mechanisms face a fundamental \emph{trilemma}: no policy can simultaneously satisfy exchange \emph{solvency}, \emph{revenue}, and \emph{fairness} to traders. This impossibility theorem implies that as participation scales, a novel form of \emph{moral hazard} grows asymptotically, rendering `zero-loss' socialization impossible. Constructively, we show that three classes of ADL mechanisms can optimally navigate this trilemma to provide fairness, robustness to price shocks, and maximal exchange revenue. We analyze these mechanisms on the Hyperliquid dataset from October 10, 2025, when ADL was used repeatedly to close \2.1 billion of positions in 12 minutes. By comparing our ADL mechanisms to the standard approaches used in practice, we demonstrate empirically that Hyperliquid's production queue overutilized ADL by approximately $8\times$ relative to our optimal policy, imposing roughly \$630 million of unnecessary haircuts on winning traders. This comparison also suggests that Binance overutilized ADL far more than Hyperliquid. Our results both theoretically and empirically demonstrate that optimized ADL mechanisms can dramatically reduce the loss of trader profits while maintaining exchange solvency.

The Solvency Capital Requirement (SCR) calculation under Solvency II is computationally intensive, relying on the estimation of own funds. Regulation mandates the direct estimation method. It has been proven that under specific assumptions, the indirect method results in the same estimate. We study their comparative properties and give novel insights. First, we provide a straightforward proof that the direct and indirect estimators for own funds converge to the same value. Second, we introduce a novel family of mixed estimators that encompasses the direct and indirect methods as its edge cases. Third, we leverage these estimators to develop powerful variance reduction techniques, constructing a single control variate from the direct and indirect estimators and a multi-control variate framework using subsets of the mixed family. These techniques can be combined with existing methods like Least-Squares Monte Carlo. We evaluate the estimators on three simplified asset-liability management models of a German life insurer, Bauer's model MUST and IS case from Bauer et al. (2006), and openIRM by Wolf et al. (2025). Our analysis confirms that neither the direct nor indirect estimator is universally superior, though the indirect method consistently outperforms the direct one in more realistic settings. The proposed control variate techniques show significant potential, in some cases reducing variance to one-tenth of that from the standard direct estimator. However, we also identify scenarios where improvements are marginal, highlighting the model-dependent nature of their efficacy. The source code is publicly available at this https URL.

We develop a statistical framework for risk estimation, inspired by the axiomatic theory of risk measures. Coherent risk estimators -- functionals of P&L samples inheriting the economic properties of risk measures -- are defined and characterized through robust representations linked to $L$-estimators. The framework provides a canonical methodology for constructing estimators with sound financial and statistical properties, unifying risk measure theory, principles for capital adequacy, and practical statistical challenges in market risk. A numerical study illustrates the approach, focusing on expected shortfall estimation under both i.i.d. and overlapping samples relevant for regulatory FRTB model applications.

In an environment of increasingly volatile financial markets, the accurate estimation of risk remains a major challenge. Traditional econometric models, such as GARCH and its variants, are based on assumptions that are often too rigid to adapt to the complexity of the current market dynamics. To overcome these limitations, we propose a hybrid framework for Value-at-Risk (VaR) estimation, combining GARCH volatility models with deep reinforcement learning. Our approach incorporates directional market forecasting using the Double Deep Q-Network (DDQN) model, treating the task as an imbalanced classification problem. This architecture enables the dynamic adjustment of risk-level forecasts according to market conditions. Empirical validation on daily Eurostoxx 50 data covering periods of crisis and high volatility shows a significant improvement in the accuracy of VaR estimates, as well as a reduction in the number of breaches and also in capital requirements, while respecting regulatory risk thresholds. The ability of the model to adjust risk levels in real time reinforces its relevance to modern and proactive risk management.

We introduce a framework for systemic risk modeling in insurance portfolios using jointly exchangeable arrays, extending classical collective risk models to account for interactions. We establish central limit theorems that asymptotically characterize total portfolio losses, providing a theoretical foundation for approximations in large portfolios and over long time horizons. These approximations are validated through simulation-based numerical experiments. Additionally, we analyze the impact of dependence on portfolio loss distributions, with a particular focus on tail behavior.

This study explores the integration of a representative large language model, ChatGPT, into lending decision-making with a focus on credit default prediction. Specifically, we use ChatGPT to analyse and interpret loan assessments written by loan officers and generate refined versions of these texts. Our comparative analysis reveals significant differences between generative artificial intelligence (AI)-refined and human-written texts in terms of text length, semantic similarity, and linguistic representations. Using deep learning techniques, we show that incorporating unstructured text data, particularly ChatGPT-refined texts, alongside conventional structured data significantly enhances credit default predictions. Furthermore, we demonstrate how the contents of both human-written and ChatGPT-refined assessments contribute to the models' prediction and show that the effect of essential words is highly context-dependent. Moreover, we find that ChatGPT's analysis of borrower delinquency contributes the most to improving predictive accuracy. We also evaluate the business impact of the models based on human-written and ChatGPT-refined texts, and find that, in most cases, the latter yields higher profitability than the former. This study provides valuable insights into the transformative potential of generative AI in financial services.

Trade execution on Decentralized Exchanges (DEXes) is automatic and does not require individual buy and sell orders to be matched. Instead, liquidity aggregated in pools from individual liquidity providers enables trading between cryptocurrencies. The largest DEX measured by trading volume, Uniswap V3, promises a DEX design optimized for capital efficiency. However, Uniswap V3 requires far more decisions from liquidity providers than previous DEX designs. In this work, we develop a theoretical model to illustrate the choices faced by Uniswap V3 liquidity providers and their implications. Our model suggests that providing liquidity on Uniswap V3 is highly complex and requires many considerations from a user. Our supporting data analysis of the risks and returns of real Uniswap V3 liquidity providers underlines that liquidity providing in Uniswap V3 is incredibly complicated, and performances can vary wildly. While there are simple and profitable strategies for liquidity providers in liquidity pools characterized by negligible price volatilities, these strategies only yield modest returns. Instead, significant returns can only be obtained by accepting increased financial risks and at the cost of active management. Thus, providing liquidity has become a game reserved for sophisticated players with the introduction of Uniswap V3, where retail traders do not stand a chance.

This study analysed a series of live cattle spot and futures prices from the Boi Gordo Index (BGI) in Brazil. The objective was to develop a model that best portrays this commodity's behaviour to estimate futures prices more accurately. The database created contained 2,010 daily entries in which trade in futures contracts occurred, as well as BGI spot sales in the market, from 1 December 2006 to 30 April 2015. One of the most important reasons why this type of risk needs to be measured is to set loss limits. To identify patterns in price behaviour in order to improve future transactions' results, investors must analyse fluctuations in assets' value for longer periods. Bibliographic research revealed that no other study has conducted a comprehensive analysis of this commodity using this approach. Cattle ranching is big business in Brazil given that in 2017, this sector moved 523.25 billion Brazilian reals (about 130.5 billion United States dollars). In that year, agribusiness contributed 22% of Brazil's total gross domestic product. Using the proposed risk modelling technique, economic agents can make the best decision about which options within these investors' reach produce more effective risk management. The methodology was based on Holt-Winters exponential smoothing algorithm, autoregressive integrated moving average (ARIMA), ARIMA with exogenous inputs, generalised autoregressive conditionally heteroskedastic and generalised autoregressive moving average (GARMA) models. More specifically, 5 different methods were applied that allowed a comparison of 12 different models as ways to portray and predict the BGI commodity's behaviour. The results show that GARMA with order c(2,1) and without intercept is the best model.

Uniswap is a decentralized exchange (DEX) and was first launched on November 2, 2018 on the Ethereum mainnet [1] and is part of an Ecosystem of products in Decentralized Finance (DeFi). It replaces a traditional order book type of trading common on centralized exchanges (CEX) with a deterministic model that swaps currencies (or tokens/assets) along a fixed price function determined by the amount of currencies supplied by the liquidity providers. Liquidity providers can be regarded as investors in the decentralized exchange and earn fixed commissions per trade. They lock up funds in liquidity pools for distinct pairs of currencies allowing market participants to swap them using the fixed price function. Liquidity providers take on market risk as a liquidity provider in exchange for earning commissions on each trade. Here we analyze the risk profile of a liquidity provider and the so called impermanent (unrealized) loss in particular. We provide an improved version of the commonly denoted impermanent loss function for Uniswap v2 on the semi-infinite domain. The differences between Uniswap v2 and v3 are also discussed.

In the current market practice, many cyber insurance products offer a coverage bundle for losses arising from various types of incidents, such as data breaches and ransomware attacks, and the coverage for each incident type comes with a separate limit and deductible. Although this gives prospective cyber insurance buyers more flexibility in customizing the coverage and better manages the risk exposures of sellers, it complicates the decision-making process in determining the optimal amount of risks to retain and transfer for both parties. This paper aims to build an economic foundation for these incident-specific cyber insurance products with a focus on how incident-specific indemnities should be designed for achieving Pareto optimality for both the insurance seller and buyer. Real data on cyber incidents is used to illustrate the feasibility of this approach. Several implementation improvement methods for practicality are also discussed.

Restaking protocols have aggregated billions of dollars of security by utilizing token incentives and payments. A natural question to ask is: How much security do restaked services \emph{really} need to purchase? To answer this question, we expand a model of Durvasula and Roughgarden [DR24] that includes incentives and an expanded threat model consisting of strategic attackers and users. Our model shows that an adversary with a strictly submodular profit combined with strategic node operators who respond to incentives can avoid the large-scale cascading failures of~[DR24]. We utilize our model to construct an approximation algorithm for choosing token-based incentives that achieve a given security level against adversaries who are bounded in the number of services they can simultaneously attack. Our results suggest that incentivized restaking protocols can be secure with proper incentive management.

Financial markets are of much interest to researchers due to their dynamic and stochastic nature. With their relations to world populations, global economies and asset valuations, understanding, identifying and forecasting trends and regimes are highly important. Attempts have been made to forecast market trends by employing machine learning methodologies, while statistical techniques have been the primary methods used in developing market regime switching models used for trading and hedging. In this paper we present a novel framework for the detection of regime switches within the US financial markets. Principal component analysis is applied for dimensionality reduction and the k-means algorithm is used as a clustering technique. Using a combination of cluster analysis and classification, we identify regimes in financial markets based on publicly available economic data. We display the efficacy of the framework by constructing and assessing the performance of two trading strategies based on detected regimes.

Statistical inference of the dependence between objects often relies on covariance matrices. Unless the number of features (e.g. data points) is much larger than the number of objects, covariance matrix cleaning is necessary to reduce estimation noise. We propose a method that is robust yet flexible enough to account for fine details of the structure covariance matrix. Robustness comes from using a hierarchical ansatz and dependence averaging between clusters; flexibility comes from a bootstrap procedure. This method finds several possible hierarchical structures in DNA microarray gene expression data, and leads to lower realized risk in global minimum variance portfolios than current filtering methods when the number of data points is relatively small.

Introduction: The paper addresses the challenging problem of predicting the short-term realized volatility of the Bitcoin price using order flow information. The inherent stochastic nature and anti-persistence of price pose difficulties in accurate prediction. Methods: To address this, we propose a method that transforms order flow data over a fixed time interval (snapshots) into images. The order flow includes trade sizes, trade directions, and limit order book, and is mapped into image colour channels. These images are then used to train both a simple 3-layer Convolutional Neural Network (CNN) and more advanced ResNet-18 and ConvMixer, with additionally supplementing them with hand-crafted features. The models are evaluated against classical GARCH, Multilayer Perceptron trained on raw data, and a naive guess method that considers current volatility as a prediction. Results: The experiments are conducted using price data from January 2021 and evaluate model performance in terms of root mean square error (RMSPE). The results show that our order flow representation with a CNN as a predictive model achieves the best performance, with an RMSPE of 0.85+/-1.1 for the model with aggregated features and 1.0+/-1.4 for the model without feature supplementation. ConvMixer with feature supplementation follows closely. In comparison, the RMSPE for the naive guess method was 1.4+/-3.0.

The initial Climate-Extended Risk Model (CERM) addresses the estimate of climate-related financial risk embedded within a bank loan portfolio, through a climatic extension of the Basel II IRB model. It uses a Gaussian copula model calibrated with non stationary macro-correlations in order to reflect the future evolution of climate-related financial risks. In this complementary article, we propose a stochastic forward-looking methodology to calibrate climate macro-correlation evolution from scientific climate data, for physical and transition efforts specifically. We assume a global physical and transition risk, likened to persistent greenhouse gas (GHG) concentration in the atmosphere. The economic risk is considered stationary and can therefore be calibrated with a backward-looking methodology. We present 4 key principles to model the GDP and we propose to model the economic, physical and transition effort factors with three interdependent stochastic processes allowing for a calibration with seven well defined parameters. These parameters can be calibrated using public data. This new approach means not only to evaluate climate risks without picking any specific scenario but also allows to fill the gap between current one year approach of regulatory and economic capital models and the necessarily long-term view of climate risks by designing a framework to evaluate the resulting credit loss on each step (typically yearly) of the transition path. This new approach could prove instrumental in the 2022 context of central banks weighing the pros and cons of a climate capital charge.

In this paper, we discuss aspects of model risk management in financial institutions which could be adopted by academic institutions to improve the process of conducting academic research, identify and mitigate existing limitations, decrease the possibility of erroneous results, and prevent fraudulent activities.

In the financial services industry, forecasting the risk factor distribution conditional on the history and the current market environment is the key to market risk modeling in general and value at risk (VaR) model in particular. As one of the most widely adopted VaR models in commercial banks, Historical simulation (HS) uses the empirical distribution of daily returns in a historical window as the forecast distribution of risk factor returns in the next day. The objectives for financial time series generation are to generate synthetic data paths with good variety, and similar distribution and dynamics to the original historical data. In this paper, we apply multiple existing deep generative methods (e.g., CGAN, CWGAN, Diffusion, and Signature WGAN) for conditional time series generation, and propose and test two new methods for conditional multi-step time series generation, namely Encoder-Decoder CGAN and Conditional TimeVAE. Furthermore, we introduce a comprehensive framework with a set of KPIs to measure the quality of the generated time series for financial modeling. The KPIs cover distribution distance, autocorrelation and backtesting. All models (HS, parametric and neural networks) are tested on both historical USD yield curve data and additional data simulated from GARCH and CIR processes. The study shows that top performing models are HS, GARCH and CWGAN models. Future research directions in this area are also discussed.