Efficient simulation of Lévy-driven point processes

We dene four classes of point processes which we call A, B, *A, *B. Although we study point processes on R; these classes are suitable for generalizations for point processes on Rm and other measure metric spaces. The main result is the equivalence of classes *A and *B for point processes on R: As a matter of fact, we prove that A B A = B S; where S is the class of simple processes. We also relate these classes and the class of Poisson processes.

This chapter is a tutorial on portfolio risk management. It describes how to identify the primary sources of risk in complex portfolios—the “hot spots”—and how to identify the trades that will reduce those risks—the “hedges.” While this topic, identifying and reducing risk, would seem to be at the heart of risk management, many of the ideas presented here are not well-understood. Unfortunately, too much of the recent focus in risk management has been directed elsewhere—for example, toward under-standing and incorporating the risks of derivative securities. While derivtives can create complex and highly nonlinear payoffs, they are often not the primary source of risk in a portfolio. Also, while risk managers have focused much attention recently on developing firm wide systems to aggregate information from many traders or portfolio managers, they have generally not yet concentrated on how to use that information to obtain a comprehensive understanding of enterprise risk. More generally, while risk managers have also recently developed a greater appreciation of the statistical nature of risk and the need to use statistical measures such as value-at-risk (VaR)1 to quantify, monitor, and set limits on risk-taking activities, the tools required to understand and incorporate these statistical measures in portfolio risk management have lagged behind.2 This most important area of risk management—the development of portfolio analytics based on the statistical understanding of risk—has not received as much attention as it deserves. We hope this chapter helps to address this concern by describing a number of portfolio analysis tools that we have developed at Goldman Sachs in recent years to better understand, manage, and monitor the risks in our clients’ investment portfolios as well as our own trading positions. We focus on the concepts of risk management and how they apply in realistic trading and portfolio management contexts rather than on details of implementation.

Integrated Volatility and UHF-GARCH Models: A Comparison Using High Frequency Financial Data

A class of point processes is considered, in which the locations of the points are independent random variables. In particular some properties of the process in which the distribution function of the position of the nth event is the n-fold convolution of some distribution function F, are investigated. It is shown that, under fairly general conditions, the process remote from the origin will be asymptotically Poisson. It is also shown that the variance of the number of events in the interval (0, t] is . Some generalisations are discussed.

Kripto varlıklar pay senetleri ve emtialar gibi geleneksel yatırım araçlarıyla karşılaştırıldığında daha az düzenleme, düşük işlem maliyetleri, merkeziyetsizlik gibi bazı avantajlara sahiptirler. Kripto varlıklar ortaya çıkışlarından günümüze kadar fiyat, hacim ve değer bakımından artarak portföylerde kendilerine yer edinmeye başlamışlardır. Kripto varlıkların geleneksel yatırım araçlarıyla olan ilişkileri portföy yönetimi açısından sonuçlar ortaya çıkarabilir. Bu çalışmada bitcoin ile altın, petrol, doğal gaz ve emtia endeksinden oluşan emtialar arasındaki volatilite yayılımları incelenmiştir. Çalışmada 24 Ağustos 2016 – 13 Ocak 2023 dönemine ait günlük veriler varyansta nedensellik ve Lu, Hong, Wang, Lai ve Liu (2014) tarafından geliştirilen zamanla değişen varyansta nedensellik testiyle incelenmiştir. Çalışmada bitcoinden altın ve emtia endeksine doğru ve doğal gazdan bitcoine doğru tek yönlü volatilite yayılımı görülmüştür. Bitcoin ile emtilar arasında düşük düzeyde zamanla değişen volatilite yayılımı belirlenmiştir. Sonuçlar portföy yönetimi, portföy riskinin yönetilmesi, yatırım kararları açısından önem taşımaktadır.

The assessment and prediction of the impact of risks on the financial performance of portfolios is a very challenging task, and many portfolios in Qatar and worldwide are still suffering from cost overruns. This aspect is undeveloped in the body of literature on portfolio risk management, and very few studies have addressed this need. Therefore, organisations and portfolio managers are still looking for tools and techniques which enable them to incorporate the financial impacts of risks during the estimation of the cost and contract price of their portfolios. In this paper, a risk management-based methodology for the prediction of the cost and the financial performance of portfolios is presented and tested on real case studies based at Qatar Gas. The methodology is based on calculating the combined effect of multiple risks on the different work packages composing part the portfolio project, while considering the probabilistic occurrence of each risk. The methodology was tested on four projects in Qatar Gas and proved to be able to predict the effect of the identified risks on financial performance related to each portfolio. It also helped to prioritize the risks and identify the risks that most affected the financial performance of the portfolio and, thus, provide valuable information for particular stages of response planning. One of the limitations of the proposed methodology is that it calculates the impact of risks on the financial performance of a portfolio at a specific date, where risk impacts have a defined probabilistic distribution. However, the dynamic nature of risk attributes could be reflected by changing the values of those attributes in the risk management model of the portfolio every time the risk register is updated.

A critical issue of diversification in portfolio management is the intra and inter-sectoral spread of risk. The aim of this study is to capture potential intra and inter sectoral risk spread. In this regard, the Bayesian Neural Networks (BNN) model was involved, the method being applied for a portfolio of 12 shares from the American index S&P 500, on the period January 1st, 2011 – January 28th, 2023. The expected shortfall was involved as a risk estimation measure and the Tabu Search learning algorithm of BNN was employed. The robustness of the results was tested at three significance thresholds namely, 0.85, 0.90 and 0.95. The differences of the results were highlighted on two subsamples, from January 1st, 2011 – December 31st, 2019, and January 1st, 2020 – January 28th, 2023. Evidence of intra and inter sectoral contagion was found on the full sample period, however during the financial turmoil period represented by the last sub-sample, the results display that the linkages between different sectors weakened to certain extents. The key contribution stands in the significant implications for portfolio risk management. The results highlight and strengthen the importance of building a portfolio based on an accurate selection of assets that are not inter-linked.

An empirical investigation on how portfolio risk management influences project portfolio success

Our poster presents a research in progress conducted together with a FTSE 100 company aiming at reaching a higher level of maturity of their ITPPM process. This process was redesigned according to best practices and analyzed using the CommonKADS methodology. This work uncovered important shortcomings in the knowledge related to project and portfolio risk management. To enable appropriate understanding and management of risk at project and portfolio level, we designed a model for risk analysis which led us to specification, deployment (integration in the company's ITPPM portal) and evaluation of a risk Knowledge Base (KB).

The financial industry's rapid adoption of artificial intelligence (AI) for portfolio risk assessment creates a tension between predictive power and explainability—a critical concern for fiduciary obligations. This research explores the implementation of explainable AI (XAI) methodologies in portfolio risk management, comparing traditional black-box models with transparent alternatives. We evaluate LIME, SHAP, and rule-based explainers against complex neural networks and ensemble methods across diverse market conditions using a comprehensive dataset of financial instruments. Results demonstrate that XAI approaches can achieve 92.4% of black-box performance while providing interpretable insights, satisfying regulatory requirements without significant accuracy sacrifices. Our framework integrates explainability metrics with performance indicators, creating a balanced scorecard for model selection in financial contexts. This work addresses the growing demand for transparent AI in financial decision-making, offering practical guidance for portfolio managers navigating the intersection of advanced analytics and fiduciary responsibility.

Is Bitcoin the New Digital Gold? Evidence From Extreme Price Movements in Financial Markets

A Slightly Depressing Jump Model: Intraday Volatility Pattern Simulation

This study examines the spillover effects of global Bitcoin (BTC), price volatility on Vietnamese stock and gold markets using daily data from 2018 to 2025 (Akpan, 2024; Umoru et al., 2025). Building on a baseline framework of ordinary least squares (OLS), fixed-effects, and instrumental variable regressions with lagged Bitcoin returns, we analyze how global Bitcoin price movements co-move with the Ho Chi Minh Stock Exchange index (VNINDEX), Hanoi Stock Exchange (HNX), and VND-denominated gold returns after controlling for USD/VND exchange rate, United States (US) 10-year treasury yields, volatility index (VIX), and turnover volatility. To capture event-driven dynamics, we further incorporate dummy variables and interaction terms around major crypto-specific events (such as regulatory announcements and large market corrections), allowing us to test whether spillovers intensify during stress periods (Umoru et al., 2025). The results indicated that although preliminary estimates suggest positive comovements, these effects weaken after robustness checks, and no significant or stable spillover from Bitcoin to Vietnamese stock or gold markets is detected. These findings challenge the view of gold as a safe haven in the Vietnamese context and point to limited diversification benefits when combining Bitcoin, stocks, and gold in domestic portfolios. Overall, the study contributes to the emerging literature on cryptocurrency spillovers in frontier markets and provides actionable insights for investors and regulators concerned with systemic risk and portfolio risk management (Chutipat et al., 2023).

This paper examines the evolution of correlations between major Gulf Cooperation Council (GCC) equity indices, namely TASI of Saudi Arabia, DFM of Dubai, and QE of Qatar, and global benchmarks, specifically the S&P 500 and MSCI World, from January 2005 to June 2025. Using regressions on monthly returns, the study evaluates correlations and betas across three subperiods: the pre-oil crash period from 2005 to 2014, the post-oil crash period from 2014 to 2020, and the post-COVID period from 2020 to 2025. Results show that TASI and DFM became more correlated with global indices after 2014, but the evidence does not establish causality. The increase may have reflected broader reforms such as liberalization of foreign ownership rules, the inclusion of Saudi Arabia in MSCI Emerging Markets, and enhanced transparency. Post-COVID, correlations plateaued for TASI and declined for DFM, likely due to renewed domestic trading dominance and regional economic divergence from global recovery patterns. By contrast, QE exhibited persistently weak and statistically insignificant linkages with global benchmarks across all periods. These findings underscore the heterogeneity of GCC markets, the conditional nature of global integration, and implications for diversification, portfolio risk management, and policy design.

PurposeThe demographic risk is the risk due to the uncertainty in the demographic scenario assumptions by which life insurance products are designed and valued. The uncertainty lies both in the accidental (insurance risk) and systematic (longevity risk) deviations of the number of deaths from the value anticipated for it. This last component gives rise to the risk due to the randomness in the choice of the survival model for valuations (model risk or projection risk). If the insurance risk component can be assumed negligible for well‐diversified portfolios, as in the case of pension annuities, longevity risk is crucial in the actuarial valuations. The question is particularly decisive in contexts in which the longevity phenomenon of the population is strong and pension annuity portfolios constitute a meaningful slice of the financial market – both typical elements of Western economies. The paper aims to focus on the solvency appraisal for a portfolio of life annuities, deepening the impact of the demographic risk according to suitable risk indexes apt to describe its evolution in time.Design/methodology/approachThe financial quantity proposed for representing the economic wealth of the life insurance company is the stochastic surplus, and the paper analyses the impact on it of different demographic assumptions by means of risk indicators as the projection risk index, the quantile surplus valuation and the ruin probability. By means of the proposed models, the longevity risk is mainly taken into account in a stochastic scenario for the financial risk component, in order to consider their interactions, too. In order to furnish practical details significant in the portfolio risk management, several numerical applications clarify the practical meaning of the models in the solvency context.FindingsThis paper studies the impact on the portfolio surplus of the systematic demographic risk, taking into account their interaction with the financial risk sources. In this order of ideas, the internal risk profile of a life annuity portfolio is deeply investigated by means of suitable risk indexes: in a solvency analysis perspective, some possible scenarios for the evolution of death rates (generated by different survival models) are considered and this paper evaluates the impact on the portfolio surplus caused by different choices of the demographic model. The first index is deduced by a variance decomposition formula, the other ones involve the conditional quantile calculus and the ruin probability. Such indexes constitute benchmarks, whose conjoined use provides useful information to the meeting of the solvency requirements.Originality/valueWith respect to the recent actuarial literature, in which the most important contribution on the surplus analysis has been given by Lisenko et al. – where the analysis focuses on the financial aspect applied to portfolios of temporary and endowment contracts – the paper considers life annuity portfolios, taking into account the effect of the systematic demographic risk and its interactions with the financial risk components.