A major concern when dealing with financial time series involving a wide variety of market risk factors is the presence of anomalies. These induce a miscalibration of the models used to quantify and manage risk, resulting in potential erroneous risk measures. We propose an approach that aims to improve anomaly detection in financial time series, overcoming most of the inherent difficulties. Valuable features are extracted from the time series by compressing and reconstructing the data through principal component analysis. We then define an anomaly score using a feedforward neural network. A time series is considered to be contaminated when its anomaly score exceeds a given cutoff value. This cutoff value is not a hand-set parameter but rather is calibrated as a neural network parameter throughout the minimization of a customized loss function. The efficiency of the proposed approach compared to several well-known anomaly detection algorithms is numerically demonstrated on both synthetic and real data sets, with high and stable performance being achieved with the PCA NN approach. We show that value-at-risk estimation errors are reduced when the proposed anomaly detection model is used with a basic imputation approach to correct the anomaly.

Within the new Basel regulatory and capital framework for market risks (FRTB, 2016), the Basel Committee on Banking Supervision’s (BCBS’s) sets out significant revisions to the market risk capital requirements framework. Key areas include moving from

The market risk measurement of a trading portfolio in banks, specifically the practical implementation of the value-at-risk (VaR) and expected shortfall (ES) models, involves intensive recalls of the pricing engine. Machine learning algorithms may offer a solution to this challenge. In this study, we investigate the application of the Gaussian process (GP) regression and multi-fidelity modeling technique as approximation for the pricing engine. More precisely, multi-fidelity modeling combines models of different fidelity levels, defined as the degree of detail and precision offered by a predictive model or simulation, to achieve rapid yet precise prediction. We use the regression models to predict the prices of mono- and multi-asset equity option portfolios. In our numerical experiments, conducted with data limitation, we observe that both the standard GP model and multi-fidelity GP model outperform both the traditional approaches used in banks and the well-known neural network model in term of pricing accuracy as well as risk calculation efficiency.

Regulatory scrutiny of banks’ internal models has intensified, demanding improvements in quantitative risk methodologies and the implementation of new regulatory measures. Repeated portfolio revaluation makes these calculations computationally challenging, notably under the Fundamental Review of the Trading Book (FRTB). In this context, we examine the computational implementation of market risk models, focusing on the practical calculation of Value at Risk (VaR) and Expected Shortfall (ES). Given the complexity of trading portfolios, these models rely on proxies and simplifying assumptions for computational efficiency. This paper explores the use of Gaussian processes (GPs), a powerful machine learning technique, to accelerate the revaluation of derivative portfolios. Trained on datasets generated by sophisticated pricing models, the GP algorithm learns valuation functions and subsequently performs rapid and accurate revaluations. Numerical tests on an equity derivatives portfolio demonstrate that Gaussian process regression (GPR) significantly reduces computation time while maintaining a high accuracy for market risk assessment.

A major concern when dealing with financial time series involving a wide variety ofmarket risk factors is the presence of anomalies. These induce a miscalibration of the models used toquantify and manage risk, resulting in potential erroneous risk measures. We propose an approachthat aims to improve anomaly detection in financial time series, overcoming most of the inherentdifficulties. Valuable features are extracted from the time series by compressing and reconstructingthe data through principal component analysis. We then define an anomaly score using a feedforwardneural network. A time series is considered to be contaminated when its anomaly score exceeds agiven cutoff value. This cutoff value is not a hand-set parameter but rather is calibrated as a neuralnetwork parameter throughout the minimization of a customized loss function. The efficiency of theproposed approach compared to several well-known anomaly detection algorithms is numericallydemonstrated on both synthetic and real data sets, with high and stable performance being achievedwith the PCA NN approach. We show that value-at-risk estimation errors are reduced when theproposed anomaly detection model is used with a basic imputation approach to correct the anomaly.

Counterparty risk, which combines market and credit risks, gained prominence after the 2008 financial crisis due to its complexity and systemic implications. Traditional management methods, such as netting and collateralization, have become computationally demanding under frameworks like the Fundamental Review of the Trading Book (FRTB). This paper explores the combined application of Gaussian process regression (GPR) and Bayesian quadrature (BQ) to enhance the efficiency and accuracy of counterparty risk metrics, particularly credit valuation adjustment (CVA). This approach balances excellent precision with significant computational performance gains. Focusing on fixed-income derivatives portfolios, such as interest rate swaps and swaptions, within the One-Factor Linear Gaussian Markov (LGM-1F) model framework, we highlight three key contributions. First, we approximate swaption prices using Bachelier’s formula, showing that forward-starting swap rates can be modeled as Gaussian dynamics, enabling efficient CVA computations. Second, we demonstrate the practical relevance of an analytical approximation for the CVA of an interest rate swap portfolio. Finally, the combined use of Gaussian processes and Bayesian quadrature underscores a powerful synergy between precision and computational efficiency, making it a valuable tool for credit risk management.