CyberSec Research

The CAPM regression is typically interpreted as if the market return contemporaneously \emph{causes} individual returns, motivating beta-neutral portfolios and factor attribution. For realized equity returns, however, this interpretation is inconsistent: a same-period arrow $R_{m,t} \to R_{i,t}$ conflicts with the fact that $R_m$ is itself a value-weighted aggregate of its constituents, unless $R_m$ is lagged or leave-one-out -- the ``aggregator contradiction.'' We formalize CAPM as a structural causal model and analyze the admissible three-node graphs linking an external driver $Z$, the market $R_m$, and an asset $R_i$. The empirically plausible baseline is a \emph{fork}, $Z \to \{R_m, R_i\}$, not $R_m \to R_i$. In this setting, OLS beta reflects not a causal transmission, but an attenuated proxy for how well $R_m$ captures the underlying driver $Z$. Consequently, ``beta-neutral'' portfolios can remain exposed to macro or sectoral shocks, and hedging on $R_m$ can import index-specific noise. Using stylized models and large-cap U.S.\ equity data, we show that contemporaneous betas act like proxies rather than mechanisms; any genuine market-to-stock channel, if at all, appears only at a lag and with modest economic significance. The practical message is clear: CAPM should be read as associational. Risk management and attribution should shift from fixed factor menus to explicitly declared causal paths, with ``alpha'' reserved for what remains invariant once those causal paths are explicitly blocked.

We derive some rather general, but complicated, formulae to compute the survival function and the first passage time distribution of the $n^\text{th}$ coordinate of a many-body stochastic process in the presence of a killing barrier. First we will study the case of two coordinates and then we will generalize the results to three or more coordinates. Even if the results are difficult to implement, we will provide examples of their use applying them to a physical system, the single file diffusion, and to the financial problem of pricing a $n^\text{th}$-to-default credit default swap ($n^\text{th}$-CDS)

This study investigates the pretrained RNN attention models with the mainstream attention mechanisms such as additive attention, Luong's three attentions, global self-attention (Self-att) and sliding window sparse attention (Sparse-att) for the empirical asset pricing research on top 420 large-cap US stocks. This is the first paper on the large-scale state-of-the-art (SOTA) attention mechanisms applied in the asset pricing context. They overcome the limitations of the traditional machine learning (ML) based asset pricing, such as mis-capturing the temporal dependency and short memory. Moreover, the enforced causal masks in the attention mechanisms address the future data leaking issue ignored by the more advanced attention-based models, such as the classic Transformer. The proposed attention models also consider the temporal sparsity characteristic of asset pricing data and mitigate potential overfitting issues by deploying the simplified model structures. This provides some insights for future empirical economic research. All models are examined in three periods, which cover pre-COVID-19 (mild uptrend), COVID-19 (steep uptrend with a large drawdown) and one year post-COVID-19 (sideways movement with high fluctuations), for testing the stability of these models under extreme market conditions. The study finds that in value-weighted portfolio back testing, Model Self-att and Model Sparse-att exhibit great capabilities in deriving the absolute returns and hedging downside risks, while they achieve an annualized Sortino ratio of 2.0 and 1.80 respectively in the period with COVID-19. And Model Sparse-att performs more stably than Model Self-att from the perspective of absolute portfolio returns with respect to the size of stocks' market capitalization.

Environmental, Social, and Governance (ESG) factors aim to provide non-financial insights into corporations. In this study, we investigate whether we can extract relevant ESG variables to assess corporate risk, as measured by logarithmic volatility. We propose a novel Hierarchical Variable Selection (HVS) algorithm to identify a parsimonious set of variables from raw data that are most relevant to risk. HVS is specifically designed for ESG datasets characterized by a tree structure with significantly more variables than observations. Our findings demonstrate that HVS achieves significantly higher performance than models using pre-aggregated ESG scores. Furthermore, when compared with traditional variable selection methods, HVS achieves superior explanatory power using a more parsimonious set of ESG variables. We illustrate the methodology using company data from various sectors of the US economy.

This paper explores the bifurcative dynamics of an artificial stock market exchange (ASME) with endogenous, myopic traders interacting through a limit order book (LOB). We showed that agent-based price dynamics possess intrinsic bistability, which is not a result of randomness but an emergent property of micro-level trading rules, where even identical initial conditions lead to qualitatively different long-run price equilibria: a deterministic zero-price state and a persistent positive-price equilibrium. The study also identifies a metastable region with elevated volatility between the basins of attraction and reveals distinct transient behaviors for trajectories converging to these equilibria. Furthermore, we observe that the system is neither entirely regular nor fully chaotic. By highlighting the emergence of divergent market outcomes from uniform beginnings, this work contributes a novel perspective on the inherent path dependence and complex dynamics of artificial stock markets.

Random-expiry options are nontraditional derivative contracts that may expire early based on a random event. We develop a methodology for pricing these options using a trinomial tree, where the middle path is interpreted as early expiry. We establish that this approach is free of arbitrage, derive its continuous-time limit, and show how it may be implemented numerically in an efficient manner.

Statistical arbitrages (StatArbs) driven by machine learning has garnered considerable attention in both academia and industry. Nevertheless, deep-learning (DL) approaches to directly exploit StatArbs in options markets remain largely unexplored. Moreover, prior graph learning (GL) -- a methodological basis of this paper -- studies overlooked that features are tabular in many cases and that tree-based methods outperform DL on numerous tabular datasets. To bridge these gaps, we propose a two-stage GL approach for direct identification and exploitation of StatArbs in options markets. In the first stage, we define a novel prediction target isolating pure arbitrages via synthetic bonds. To predict the target, we develop RNConv, a GL architecture incorporating a tree structure. In the second stage, we propose SLSA -- a class of positions comprising pure arbitrage opportunities. It is provably of minimal risk and neutral to all Black-Scholes risk factors under the arbitrage-free assumption. We also present the SLSA projection converting predictions into SLSA positions. Our experiments on KOSPI 200 index options show that RNConv statistically significantly outperforms GL baselines, and that SLSA consistently yields positive returns, achieving an average P&L-contract information ratio of 0.1627. Our approach offers a novel perspective on the prediction target and strategy for exploiting StatArbs in options markets through the lens of DL, in conjunction with a pioneering tree-based GL.

This paper considers the difference of stop-loss payoffs where the underlying is a difference of two random variables. The goal is to study whether the comonotonic and countermonotonic modifications of those two random variables can be used to construct upper and lower bounds for the expected payoff, despite the fact that the payoff function is neither convex nor concave. The answer to the central question of the paper requires studying the crossing points of the cdf of the original difference with the cdfs of its comonotonic and countermonotonic transforms. The analysis is supplemented with a numerical study of longevity trend bonds, using different mortality models and population data. The numerical study reveals that for these mortality-linked securities the three pairs of cdfs generally have unique pairwise crossing points. Under symmetric copulas, all crossing points can reasonably be approximated by the difference of the marginal medians, but this approximation is not necessarily valid for asymmetric copulas. Nevertheless, extreme dependence structures can give rise to bounds if the layers of the bond are selected to hedge tail risk. Further, the dependence uncertainty spread can be low if the layers are selected to hedge median risk, and, subject to a trade-off, to hedge tail risk as well.

We revisit the stochastic collocation method using the exponential of a quadratic spline. In particular, we look in details whether it is more appropriate to fix the ordinates and optimize the abscissae of an interpolating spline or to fix the abscissae and optimize the parameters of a B-spline representation.

We review Markov models of surplus in life insurance based on a counting process following Norberg (1991), uniting probabilistic theory with elements of practice largely drawn from UK experience. First, we organize models systematically based on one and two technical bases, including a suitable descriptive notation. Extending this to three technical bases to accommodate different valuation approaches leads us: (a) to expand the definition of 'technical basis' to include non-contractual cashflows recognized in the associated Thiele equation; and (b) to add new (mainly) systematic terms to the surplus. Making these cashflows dynamic or 'quasi-contractual' covers many real applications, and we give two as examples, the paid-up valuation principle and reversionary bonus on participating contracts.

Traditional models for pricing catastrophe (CAT) bonds struggle to capture the complex, relational data inherent in these instruments. This paper introduces CATNet, a novel framework that applies a geometric deep learning architecture, the Relational Graph Convolutional Network (R-GCN), to model the CAT bond primary market as a graph, leveraging its underlying network structure for spread prediction. Our analysis reveals that the CAT bond market exhibits the characteristics of a scale-free network, a structure dominated by a few highly connected and influential hubs. CATNet demonstrates high predictive performance, significantly outperforming a strong Random Forest benchmark. The inclusion of topological centrality measures as features provides a further, significant boost in accuracy. Interpretability analysis confirms that these network features are not mere statistical artifacts; they are quantitative proxies for long-held industry intuition regarding issuer reputation, underwriter influence, and peril concentration. This research provides evidence that network connectivity is a key determinant of price, offering a new paradigm for risk assessment and proving that graph-based models can deliver both state-of-the-art accuracy and deeper, quantifiable market insights.

The Marketron model, introduced by [Halperin, Itkin, 2025], describes price formation in inelastic markets as the nonlinear diffusion of a quasiparticle (the marketron) in a multidimensional space comprising the log-price $x$, a memory variable $y$ encoding past money flows, and unobservable return predictors $z$. While the original work calibrated the model to S\&P 500 time series data, this paper extends the framework to option markets - a fundamentally distinct challenge due to market incompleteness stemming from non-tradable state variables. We develop a utility-based pricing approach that constructs a risk-adjusted measure via the dual solution of an optimal investment problem. The resulting Hamilton-Jacobi-Bellman (HJB) equation, though computationally formidable, is solved using a novel methodology enabling efficient calibration even on standard laptop hardware. Having done that, we look at the additional question to answer: whether the Marketron model, calibrated to market option prices, can simultaneously reproduce the statistical properties of the underlying asset's log-returns. We discuss our results in view of the long-standing challenge in quantitative finance of developing an unified framework capable of jointly capturing equity returns, option smile dynamics, and potentially volatility index behavior.

A multi-factor extension of the Hobson and Rogers (HR) model, incorporating a quadratic variance function (QHR model), is proposed and analysed. The QHR model allows for greater flexibility in defining the moving average filter while maintaining the Markovian property of the original HR model. The use of a quadratic variance function permits the characterisation of weak-stationarity conditions for the variance process and allows for explicit expressions for forward variance. Under the assumption of stationarity, both the variance and the squared increment processes exhibit an ARMA autocorrelation structure. The stationary distribution of the prototypical scalar QHR model is that of a translated and rescaled Pearson type IV random variable. A numerical exercise illustrates the qualitative properties of the QHR model, including the implied volatility surface and the term structures of forward variance, at-the-money (ATM) volatility, and ATM skew.

This paper examines systematic put-writing strategies applied to S&P 500 Index options, with a focus on position sizing as a key determinant of long-term performance. Despite the well-documented volatility risk premium, where implied volatility exceeds realized volatility, the practical implementation of short-dated volatility-selling strategies remains underdeveloped in the literature. This study evaluates three position sizing approaches: the Kelly criterion, VIX-based volatility regime scaling, and a novel hybrid method combining both. Using SPXW options with expirations from 0 to 5 days, the analysis explores a broad design space, including moneyness levels, volatility estimators, and memory horizons. Results show that ultra-short-dated, far out-of-the-money options deliver superior risk-adjusted returns. The hybrid sizing method consistently balances return generation with robust drawdown control, particularly under low-volatility conditions such as those seen in 2024. The study offers new insights into volatility harvesting, introducing a dynamic sizing framework that adapts to shifting market regimes. It also contributes practical guidance for constructing short-dated option strategies that are robust across market environments. These findings have direct applications for institutional investors seeking to enhance portfolio efficiency through systematic exposure to volatility premia.

In this paper we study the quality of model-free valuation approaches for financial derivatives by systematically evaluating the difference between model-free super-hedging strategies and the realized payoff of financial derivatives using historical option prices from several constituents of the S&P 500 between 2018 and 2022. Our study allows in particular to describe the realized gap between payoff and model-free hedging strategy empirically so that we can quantify to which degree model-free approaches are overly conservative. Our results imply that the model-free hedging approach is only marginally more conservative than industry-standard models such as the Heston-model while being model-free at the same time. This finding, its statistical description and the model-independence of the hedging approach enable us to construct an explicit trading strategy which, as we demonstrate, can be profitably applied in financial markets, and additionally possesses the desirable feature with an explicit control of its downside risk due to its model-free construction preventing losses pathwise.

We study an overlapping generations (OLG) exchange economy with an asset that yields dividends. First, we derive general conditions, based on exogenous parameters, that give rise to three distinct scenarios: (1) only bubbleless equilibria exist, (2) a bubbleless equilibrium coexists with a continuum of bubbly equilibria, and (3) all equilibria are bubbly. Under stationary endowments and standard assumptions, we provide a complete characterization of the equilibrium set and the associated asset price dynamics. In this setting, a bubbly equilibrium exists if and only if the interest rate in the economy without the asset is strictly lower than the population growth rate and the sum of per capita dividends is finite. Second, we establish necessary and sufficient conditions for Pareto optimality. Finally, we investigate the relationship between asset price behaviors and the optimality of equilibria.

This paper mathematically models a constant-function automated market maker (CFAMM) position as a portfolio of exotic options, known as perpetual American continuous-installment (CI) options. This model replicates an AMM position's delta at each point in time over an infinite time horizon, thus taking into account the perpetual nature and optionality to withdraw of liquidity provision. This framework yields two key theoretical results: (a) It proves that the AMM's adverse-selection cost, loss-versus-rebalancing (LVR), is analytically identical to the continuous funding fees (the time value decay or theta) earned by the at-the-money CI option embedded in the replicating portfolio. (b) A special case of this model derives an AMM liquidity position's delta profile and boundaries that suffer approximately constant LVR, up to a bounded residual error, over an arbitrarily long forward window. Finally, the paper describes how the constant volatility parameter required by the perpetual option can be calibrated from the term structure of implied volatilities and estimates the errors for both implied volatility calibration and LVR residual error. Thus, this work provides a practical framework enabling liquidity providers to choose an AMM liquidity profile and price boundaries for an arbitrarily long, forward-looking time window where they can expect an approximately constant, price-independent LVR. The results establish a rigorous option-theoretic interpretation of AMMs and their LVR, and provide actionable guidance for liquidity providers in estimating future adverse-selection costs and optimizing position parameters.

We develop a new framework for constructing factors from firm characteristics that balances statistical efficiency and economic interpretability. Instead of using all characteristics equally, our method groups related characteristics and derives one factor per group. The grouping combines economic intuition with data-driven clustering. Applied to the IPCA model by Kelly et al. (2019), our approach yields economically meaningful factors that match or exceed standard IPCA in pricing performance. Using 94 characteristics from Gu et al. (2020), we show that our parsimonious, transparent factors outperform benchmarks in out-of-sample tests, demonstrating the value of embedding economic structure into statistical modeling.