CyberSec Research

We show that Markowitz's (1952) decomposition of a portfolio variance as a quadratic form in the variables of the relative amounts invested into the securities, which has been the core of classical portfolio theory for more than 70 years, is valid only in the approximation when all trade volumes with all securities of the portfolio are assumed constant. We derive the market-based portfolio variance and its decomposition by its securities, which accounts for the impact of random trade volumes and is a polynomial of the 4th degree in the variables of the relative amounts invested into the securities. To do that, we transform the time series of market trades with the securities of the portfolio and obtain the time series of trades with the portfolio as a single market security. The time series of market trades determine the market-based means and variances of prices and returns of the portfolio in the same form as the means and variances of any market security. The decomposition of the market-based variance of returns of the portfolio by its securities follows from the structure of the time series of market trades of the portfolio as a single security. The market-based decompositions of the portfolio's variances of prices and returns could help the managers of multi-billion portfolios and the developers of large market and macroeconomic models like BlackRock's Aladdin, JP Morgan, and the U.S. Fed adjust their models and forecasts to the reality of random markets.

This paper proposes a new algorithm -- Trading Graph Neural Network (TGNN) that can structurally estimate the impact of asset features, dealer features and relationship features on asset prices in trading networks. It combines the strength of the traditional simulated method of moments (SMM) and recent machine learning techniques -- Graph Neural Network (GNN). It outperforms existing reduced-form methods with network centrality measures in prediction accuracy. The method can be used on networks with any structure, allowing for heterogeneity among both traders and assets.

We introduce a new machine learning approach to detect value-relevant foreign information for both domestic and multinational companies. Candidate foreign signals include lagged returns of stock markets and individual stocks across 47 foreign markets. By training over 100,000 models, we capture stock-specific, time-varying relationships between foreign signals and U.S. stock returns. Foreign signals exhibit out-of-sample return predictability for a subset of U.S. stocks across domestic and multinational companies. Valuable foreign signals are not concentrated in those largest foreign markets nor foreign firms in the same industry as U.S. firms. Signal importance analysis reveals the price discovery of foreign information is significantly slower for information from emerging and low-media-coverage markets and among stocks with lower foreign institutional ownership but is accelerated during the COVID-19 crisis. Our study suggests that machine learning-based investment strategies leveraging foreign signals can emerge as important mechanisms to improve the market efficiency of foreign information.

Long-term investing was previously seen as requiring human judgment. With the advent of generative artificial intelligence (AI) systems, automated systematic long-term investing is now feasible. In this paper, we present DBOT, a system whose goal is to reason about valuation like Aswath Damodaran, who is a unique expert in the investment arena in terms of having published thousands of valuations on companies in addition to his numerous writings on the topic, which provide ready training data for an AI system. DBOT can value any publicly traded company. DBOT can also be back-tested, making its behavior and performance amenable to scientific inquiry. We compare DBOT to its analytic parent, Damodaran, and highlight the research challenges involved in raising its current capability to that of Damodaran's. Finally, we examine the implications of DBOT-like AI agents for the financial industry, especially how they will impact the role of human analysts in valuation.

We present a general computational framework for solving continuous-time financial market equilibria under minimal modeling assumptions while incorporating realistic financial frictions, such as trading costs, and supporting multiple interacting agents. Inspired by generative adversarial networks (GANs), our approach employs a novel generative deep reinforcement learning framework with a decoupling feedback system embedded in the adversarial training loop, which we term as the \emph{reinforcement link}. This architecture stabilizes the training dynamics by incorporating feedback from the discriminator. Our theoretically guided feedback mechanism enables the decoupling of the equilibrium system, overcoming challenges that hinder conventional numerical algorithms. Experimentally, our algorithm not only learns but also provides testable predictions on how asset returns and volatilities emerge from the endogenous trading behavior of market participants, where traditional analytical methods fall short. The design of our model is further supported by an approximation guarantee.

Public announcement dates are used in the green bond literature to measure equity market reactions to upcoming green bond issues. We find a sizeable number of green bond announcements were pre-dated by anonymous information leakages on the Bloomberg Terminal. From a candidate set of 2,036 'Bloomberg News' and 'Bloomberg First Word' headlines gathered between 2016 and 2022, we identify 259 instances of green bond-related information being released before being publicly announced by the issuing firm. These pre-announcement leaks significantly alter the equity trading dynamics of the issuing firms over intraday and daily event windows. Significant negative abnormal returns and increased trading volumes are observed following news leaks about upcoming green bond issues. These negative investor reactions are concentrated amongst financial firms, and leaks that arrive pre-market or early in market trading. We find equity price movements following news leaks can be explained to a greater degree than following public announcements. Sectoral differences are also observed in the key drivers behind investor reactions to green bond leaks by non-financials (Tobin's Q and free cash flow) and financials (ROA). Our results suggest that information leakages have a strong impact on market behaviour, and should be accounted for in green bond literature. Our findings also have broader ramifications for financial literature going forward. Privileged access to financially material information, courtesy of the ubiquitous use of Bloomberg Terminals by professional investors, highlights the need for event studies to consider wider sets of communication channels to confirm the date at which information first becomes available.

Although the valuation of life contingent assets has been thoroughly investigated under the framework of mathematical statistics, little financial economics research pays attention to the pricing of these assets in a non-arbitrage, complete market. In this paper, we first revisit the Fundamental Theorem of Asset Pricing (FTAP) and the short proof of it. Then we point out that discounted asset price is a martingale only when dividends are zero under all random states of the world, using a simple proof based on pricing kernel. Next, we apply Fundamental Theorem of Asset Pricing (FTAP) to find valuation formula for life contingent assets including life insurance policies and life contingent annuities. Last but not least, we state the assumption of static portfolio in a dynamic economy, and clarify the FTAP that accommodates the valuation of a portfolio of life contingent policies.

This note outlines an approach to stress testing of covariance of financial time series, in the context of financial risk management. It discusses how the geodesic distance between covariance matrices implies a notion of plausibility of covariance stress tests. In this approach, correlation stress tests span a submanifold of constant determinant of the Fisher--Rao manifold of covariance matrices. A parsimonious geometrically invariant definition of arbitrarily large correlation stress tests is proposed, and a few examples are discussed.

This article consolidates and extends past work on derivative pricing adjustments, including XVA, by providing an encapsulating representation of the adjustment between any two derivative pricing functions, within an Ito SDE/parabolic PDE framework. We give examples of this representation encapsulating others from the past 20 years, ranging from a well known option pricing adjustment introduced by Gatheral, to the collection of semi-replication XVA originating from Burgard & Kjaer. To highlight extensions, we discuss certain meta-adjustments beyond XVA, designed to help signal and mitigate XVA model risk.

We propose a new financial model, the stochastic volatility model with sticky drawdown and drawup processes (SVSDU model), which enables us to capture the features of winning and losing streaks that are common across financial markets but can not be captured simultaneously by the existing financial models. Moreover, the SVSDU model retains the advantages of the stochastic volatility models. Since there are not closed-form option pricing formulas under the SVSDU model and the existing simulation methods for the sticky diffusion processes are really time-consuming, we develop a deep neural network to solve the corresponding high-dimensional parametric partial differential equation (PDE), where the solution to the PDE is the pricing function of a European option according to the Feynman-Kac Theorem, and validate the accuracy and efficiency of our deep learning approach. We also propose a novel calibration framework for our model, and demonstrate the calibration performances of our models on both simulated data and historical data. The calibration results on SPX option data show that the SVSDU model is a good representation of the asset value dynamic, and both winning and losing streaks are accounted for in option values. Our model opens new horizons for modeling and predicting the dynamics of asset prices in financial markets.

An important step in the Financial Benchmarks Reform was taken on 13th September 2018, when the ECB Working Group on Euro Risk-Free Rates recommended the Euro Short-Term Rate ESTR as the new benchmark rate for the euro area, to replace the Euro OverNight Index Average (EONIA) which will be discontinued at the end of 2021. This transition has a number of important consequences on financial instruments, OTC derivatives in particular. In this paper we show in detail how the switch from EONIA to ESTR affects the pricing of OIS, IRS and XVAs. We conclude that the adoption of the "clean discounting" approach recommended by the the ECB, based on ESTR only, is theoretically sound and leads to very limited impacts on financial valuations. This finding ensures the possibility, for the financial industry, to switch all EUR OTC derivatives, either cleared with Central Counterparties, or subject to bilateral collateral agreements, or non-collateralised, in a safe and consistent manner. The transition to such EONIA-free pricing framework is essential for the complete elimination of EONIA before its discontinuation scheduled on 31st December 2021.

We introduce a model for the loss distribution of a credit portfolio considering a contagion mechanism for the default of names which is the result of two independent components: an infection attempt generated by defaulting entities and a failed defence from healthy ones. We then propose an efficient recursive algorithm for the loss distribution. Then we extend the framework with a more flexible mixture distribution to better fit real-world data. Finally, we propose an empirical application in which we price synthetic CDO tranches of the iTraxx index, finding a good fit for multiple tranches.

We introduce the Volterra Stein-Stein model with stochastic interest rates, where both volatility and interest rates are driven by correlated Gaussian Volterra processes. This framework unifies various well-known Markovian and non-Markovian models while preserving analytical tractability for pricing and hedging financial derivatives. We derive explicit formulas for pricing zero-coupon bond and interest rate cap or floor, along with a semi-explicit expression for the characteristic function of the log-forward index using Fredholm resolvents and determinants. This allows for fast and efficient derivative pricing and calibration via Fourier methods. We calibrate our model to market data and observe that our framework is flexible enough to capture key empirical features, such as the humped-shaped term structure of ATM implied volatilities for cap options and the concave ATM implied volatility skew term structure (in log-log scale) of the S&P 500 options. Finally, we establish connections between our characteristic function formula and expressions that depend on infinite-dimensional Riccati equations, thereby making the link with conventional linear-quadratic models.

This paper documents new investment value in analyst reports. Analyst narratives embedded with large language models strongly forecast future stock returns, generating significant alpha beyond established analyst-based and fundamental-based factors. The return predictability arises primarily from reports that convey negative sentiment but forecast favorable long-term prospects, suggesting systematic market overreaction to near-term negative news. The effect is more pronounced for large, mature firms and for reports authored by skilled, experienced analysts. A Shapley value decomposition reveals that analysts' strategic outlook contributes the most to portfolio performance, especially forward-looking discussions on fundamentals. Beyond demonstrating untapped value in qualitative information, this paper illustrates the broader potential of artificial intelligence to augment, rather than replace, expert human judgment in financial markets.

Cryptocurrencies fluctuate in markets with high price volatility, posing significant challenges for investors. To aid in informed decision-making, systems predicting cryptocurrency market movements have been developed, typically focusing on historical patterns. However, these methods often overlook three critical factors influencing market dynamics: 1) the macro investing environment, reflected in major cryptocurrency fluctuations affecting collaborative investor behaviors; 2) overall market sentiment, heavily influenced by news impacting investor strategies; and 3) technical indicators, offering insights into overbought or oversold conditions, momentum, and market trends, which are crucial for short-term price movements. This paper proposes a dual prediction mechanism that forecasts the next day's closing price by incorporating macroeconomic fluctuations, technical indicators, and individual cryptocurrency price changes. Additionally, a novel refinement mechanism enhances predictions through market sentiment-based rescaling and fusion. Experiments demonstrate that the proposed model achieves state-of-the-art performance, consistently outperforming ten comparison methods.

In econophysics, there are several enigmatic empirical laws: (i)~the market-order flow has strong persistence (long-range order-sign correlation), well formulated as the Lillo-Mike-Farmer model. This phenomenon seems paradoxical given the diffusive and unpredictable price dynamics; (ii)~the price impact $I(Q)$ of a large metaorder $Q$ follows the square-root law, $I(Q)\propto \sqrt{Q}$. In this Letter, we propose an exactly solvable model of the nonlinear price-impact dynamics that unifies these enigmas. We generalize the Lillo-Mike-Farmer model to nonlinear price-impact dynamics, which is mapped to an exactly solvable L\'evy-walk model. Our exact solution and numerical simulations reveal three important points: First, the price dynamics remains diffusive under the square-root law, even under the long-range correlation. Second, price-movement statistics follows truncated power laws with typical exponent around three. Third, volatility has long memory. While this simple model lacks adjustable free parameters, it naturally aligns even with other enigmatic empirical laws, such as (iii)~the inverse-cubic law for price statistics and (iv)~volatility clustering. This work illustrates the crucial role of the square-root law in understanding rich and complex financial price dynamics from a single coherent viewpoint.

This study presents a comparative analysis of Monte Carlo (MC) and quasi-Monte Carlo (QMC) methods in the context of derivative pricing, emphasizing convergence rates and the curse of dimensionality. After a concise overview of traditional Monte Carlo techniques for evaluating expectations of derivative securities, the paper introduces quasi-Monte Carlo methods, which leverage low-discrepancy sequences to achieve more uniformly distributed sample points without relying on randomness. Theoretical insights highlight that QMC methods can attain superior convergence rates of $O(1/n^{1-\epsilon})$ compared to the standard MC rate of $O(1/\sqrt{n})$, where $\epsilon>0$. Numerical experiments are conducted on two types of options: geometric basket call options and Asian call options. For the geometric basket options, a five-dimensional setting under the Black-Scholes framework is utilized, comparing the performance of Sobol' and Faure low-discrepancy sequences against standard Monte Carlo simulations. Results demonstrate a significant reduction in root mean square error for QMC methods as the number of sample points increases. Similarly, for Asian call options, incorporating a Brownian bridge construction with RQMC further enhances accuracy and convergence efficiency. The findings confirm that quasi-Monte Carlo methods offer substantial improvements over traditional Monte Carlo approaches in derivative pricing, particularly in scenarios with moderate dimensionality.

In this paper, we consider scaling limits of exponential utility indifference prices for European contingent claims in the Bachelier model. We show that the scaling limit can be represented in terms of the \emph{specific relative entropy}, and in addition we construct asymptotic optimal hedging strategies. To prove the upper bound for the limit, we formulate the dual problem as a stochastic control, and show there exists a classical solution to its HJB equation. The proof for the lower bound relies on the duality result for exponential hedging in discrete time.