New articles on Quantitative Finance


[1] 2406.06552

Optimizing Sharpe Ratio: Risk-Adjusted Decision-Making in Multi-Armed Bandits

Sharpe Ratio (SR) is a critical parameter in characterizing financial time series as it jointly considers the reward and the volatility of any stock/portfolio through its variance. Deriving online algorithms for optimizing the SR is particularly challenging since even offline policies experience constant regret with respect to the best expert Even-Dar et al (2006). Thus, instead of optimizing the usual definition of SR, we optimize regularized square SR (RSSR). We consider two settings for the RSSR, Regret Minimization (RM) and Best Arm Identification (BAI). In this regard, we propose a novel multi-armed bandit (MAB) algorithm for RM called UCB-RSSR for RSSR maximization. We derive a path-dependent concentration bound for the estimate of the RSSR. Based on that, we derive the regret guarantees of UCB-RSSR and show that it evolves as O(log n) for the two-armed bandit case played for a horizon n. We also consider a fixed budget setting for well-known BAI algorithms, i.e., sequential halving and successive rejects, and propose SHVV, SHSR, and SuRSR algorithms. We derive the upper bound for the error probability of all proposed BAI algorithms. We demonstrate that UCB-RSSR outperforms the only other known SR optimizing bandit algorithm, U-UCB Cassel et al (2023). We also establish its efficacy with respect to other benchmarks derived from the GRA-UCB and MVTS algorithms. We further demonstrate the performance of proposed BAI algorithms for multiple different setups. Our research highlights that our proposed algorithms will find extensive applications in risk-aware portfolio management problems. Consequently, our research highlights that our proposed algorithms will find extensive applications in risk-aware portfolio management problems.


[2] 2406.06594

Stock Movement Prediction with Multimodal Stable Fusion via Gated Cross-Attention Mechanism

The accurate prediction of stock movements is crucial for investment strategies. Stock prices are subject to the influence of various forms of information, including financial indicators, sentiment analysis, news documents, and relational structures. Predominant analytical approaches, however, tend to address only unimodal or bimodal sources, neglecting the complexity of multimodal data. Further complicating the landscape are the issues of data sparsity and semantic conflicts between these modalities, which are frequently overlooked by current models, leading to unstable performance and limiting practical applicability. To address these shortcomings, this study introduces a novel architecture, named Multimodal Stable Fusion with Gated Cross-Attention (MSGCA), designed to robustly integrate multimodal input for stock movement prediction. The MSGCA framework consists of three integral components: (1) a trimodal encoding module, responsible for processing indicator sequences, dynamic documents, and a relational graph, and standardizing their feature representations; (2) a cross-feature fusion module, where primary and consistent features guide the multimodal fusion of the three modalities via a pair of gated cross-attention networks; and (3) a prediction module, which refines the fused features through temporal and dimensional reduction to execute precise movement forecasting. Empirical evaluations demonstrate that the MSGCA framework exceeds current leading methods, achieving performance gains of 8.1%, 6.1%, 21.7% and 31.6% on four multimodal datasets, respectively, attributed to its enhanced multimodal fusion stability.


[3] 2406.06706

Application of Black-Litterman Bayesian in Statistical Arbitrage

\begin{abstract} In this paper, we integrated the statistical arbitrage strategy, pairs trading, into the Black-Litterman model and constructed efficient mean-variance portfolios. Typically, pairs trading underperforms under volatile or distressed market condition because the selected asset pairs fail to revert to equilibrium within the investment horizon. By enhancing this strategy with the Black-Litterman portfolio optimization, we achieved superior performance compared to the S\&P 500 market index under both normal and extreme market conditions. Furthermore, this research presents an innovative idea of incorporating traditional pairs trading strategies into the portfolio optimization framework in a scalable and systematic manner.


[4] 2406.06952

Factors and moderators of ageism: An analysis using data from 55 countries in the World Values Survey Wave 6

Today, as the aging of the world accelerates, it is an urgent task to clarify factors that prevent ageism. In this study, using hierarchical multiple regression analysis of data from 40,869 people from 55 countries collected in the World Values Survey Wave 6, we showed that after controlling for demographic factors, stereotypes, a hungry spirit, and male chauvinism are related to ageism, and that altruism, trust within and outside the family, and trust in competition moderate the relationship between the independent and dependent variables. Furthermore, data from Japan, which has the highest aging rate and aging speed in the world, showed that these moderation relationships are moderated.


[5] 2406.07149

From Policy to Practice: The Cost of Europe's Green Hydrogen Ambitions

The European Commission's new definition of green hydrogen provides clear guidelines and legal certainty for producers and consumers. However, the strict criteria for electrolysis production, requiring additionality, temporal correlation, and geographical correlation, could increase hydrogen costs, affecting its competitiveness as an energy carrier. This study examines the impact of these European regulations using a stochastic capacity expansion model for the European energy market up to 2048. We analyze how these requirements influence costs and investment decisions. Our results show that green hydrogen production requirements will raise system costs by 82 Euro billion from 2024 to 2048, driven mainly by a rapid transition from fossil fuels to renewable energy. The additionality requirement, which mandates the use of new renewable energy installations for electrolysis, emerges as the most expensive to comply with but also the most effective in accelerating the transition to renewable power, particularly before 2030.


[6] 2406.07200

A Multi-step Approach for Minimizing Risk in Decentralized Exchanges

Decentralized Exchanges are becoming even more predominant in today's finance. Driven by the need to study this phenomenon from an academic perspective, the SIAG/FME Code Quest 2023 was announced. Specifically, participating teams were asked to implement, in Python, the basic functions of an Automated Market Maker and a liquidity provision strategy in an Automated Market Maker to minimize the Conditional Value at Risk, a critical measure of investment risk. As the competition's winning team, we highlight our approach in this work. In particular, as the dependence of the final return on the initial wealth distribution is highly non-linear, we cannot use standard ad-hoc approaches. Additionally, classical minimization techniques would require a significant computational load due to the cost of the target function. For these reasons, we propose a three-step approach. In the first step, the target function is approximated by a Kernel Ridge Regression. Then, the approximating function is minimized. In the final step, the previously discovered minimum is utilized as the starting point for directly optimizing the desired target function. By using this procedure, we can both reduce the computational complexity and increase the accuracy of the solution. Finally, the overall computational load is further reduced thanks to an algorithmic trick concerning the returns simulation and the usage of Cython.


[7] 2406.07210

The green hydrogen ambition and implementation gap

Green hydrogen is critical for decarbonising hard-to-electrify sectors, but faces high costs and investment risks. Here we define and quantify the green hydrogen ambition and implementation gap, showing that meeting hydrogen expectations will remain challenging despite surging announcements of projects and subsidies. Tracking 137 projects over three years, we identify a wide 2022 implementation gap with only 2% of global capacity announcements finished on schedule. In contrast, the 2030 ambition gap towards 1.5{\deg}C scenarios is gradually closing as the announced project pipeline has nearly tripled to 441 GW within three years. However, we estimate that, without carbon pricing, realising all these projects would require global subsidies of \$1.6 trillion (\$1.2 - 2.6 trillion range), far exceeding announced subsidies. Given past and future implementation gaps, policymakers must prepare for prolonged green hydrogen scarcity. Policy support needs to secure hydrogen investments, but should focus on applications where hydrogen is indispensable.


[8] 2406.07354

The Theory of Intrinsic Time: A Primer

The concept of time mostly plays a subordinate role in finance and economics. The assumption is that time flows continuously and that time series data should be analyzed at regular, equidistant intervals. Nonetheless, already nearly 60 years ago, the concept of an event-based measure of time was first introduced. This paper expands on this theme by discussing the paradigm of intrinsic time, its origins, history, and modern applications. Departing from traditional, continuous measures of time, intrinsic time proposes an event-based, algorithmic framework that captures the dynamic and fluctuating nature of real-world phenomena more accurately. Unsuspected implications arise in general for complex systems and specifically for financial markets. For instance, novel structures and regularities are revealed, otherwise obscured by any analysis utilizing equidistant time intervals. Of particular interest is the emergence of a multiplicity of scaling laws, a hallmark signature of an underlying organizational principle in complex systems. Moreover, a central insight from this novel paradigm is the realization that universal time does not exist; instead, time is observer-dependent, shaped by the intrinsic activity unfolding within complex systems. This research opens up new avenues for economic modeling and forecasting, paving the way for a deeper understanding of the invisible forces that guide the evolution and emergence of market dynamics and financial systems. An exciting and rich landscape of possibilities emerges within the paradigm of intrinsic time.


[9] 2406.07388

Probabilistic models and statistics for electronic financial markets in the digital age

The scope of this manuscript is to review some recent developments in statistics for discretely observed semimartingales which are motivated by applications for financial markets. Our journey through this area stops to take closer looks at a few selected topics discussing recent literature. We moreover highlight and explain the important role played by some classical concepts of probability and statistics. We focus on three main aspects: Testing for jumps; rough fractional stochastic volatility; and limit order microstructure noise. We review jump tests based on extreme value theory and complement the literature proposing new statistical methods. They are based on asymptotic theory of order statistics and the R\'{e}nyi representation. The second stage of our journey visits a recent strand of research showing that volatility is rough. We further investigate this and establish a minimax lower bound exploring frontiers to what extent the regularity of latent volatility can be recovered in a more general framework. Finally, we discuss a stochastic boundary model with one-sided microstructure noise for high-frequency limit order prices and its probabilistic and statistical foundation.


[10] 2406.07464

Convex ordering for stochastic control: the swing contracts case

We investigate propagation of convexity and convex ordering on a typical stochastic optimal control problem, namely the pricing of \q{\emph{Take-or-Pay}} swing option, a financial derivative product commonly traded on energy markets. The dynamics of the underlying asset is modelled by an \emph{ARCH} model with convex coefficients. We prove that the value function associated to the stochastic optimal control problem is a convex function of the underlying asset price. We also introduce a domination criterion offering insights into the monotonicity of the value function with respect to parameters of the underlying \emph{ARCH} coefficients. We particularly focus on the one-dimensional setting where, by means of Stein's formula and regularization techniques, we show that the convexity assumption for the \emph{ARCH} coefficients can be relaxed with a semi-convexity assumption. To validate the results presented in this paper, we also conduct numerical illustrations.


[11] 2406.07525

Will Southeast Asia be the next global manufacturing hub? A multiway cointegration, causality, and dynamic connectedness analyses on factors influencing offshore decisions

The COVID-19 pandemic has compelled multinational corporations to diversify their global supply chain risk and to relocate their factories to Southeast Asian countries beyond China. Such recent phenomena provide a good opportunity to understand the factors that influenced offshore decisions in the last two decades. We propose a new conceptual framework based on econometric approaches to examine the relationships between these factors. Firstly, the Vector Auto Regression (VAR) for multi-way cointegration analysis by a Johansen test as well as the embedding Granger causality analysis to examine offshore decisions--innovation, technology readiness, infrastructure, foreign direct investment (FDI), and intermediate imports. Secondly, a Quantile Vector Autoregressive (QVAR) model is used to assess the dynamic connectedness among Southeast Asian countries based on the offshore factors. This study explores a system-wide experiment to evaluate the spillover effects of offshore decisions. It reports a comprehensive analysis using time-series data collected from the World Bank. The results of the cointegration, causality, and dynamic connectedness analyses show that a subset of Southeast Asian countries have spillover effects on each other. These countries present a multi-way cointegration and dynamic connectedness relationship. The study contributes to policymaking by providing a data-driven innovative approach through a new conceptual framework.


[12] 2406.06860

Cluster GARCH

We introduce a novel multivariate GARCH model with flexible convolution-t distributions that is applicable in high-dimensional systems. The model is called Cluster GARCH because it can accommodate cluster structures in the conditional correlation matrix and in the tail dependencies. The expressions for the log-likelihood function and its derivatives are tractable, and the latter facilitate a score-drive model for the dynamic correlation structure. We apply the Cluster GARCH model to daily returns for 100 assets and find it outperforms existing models, both in-sample and out-of-sample. Moreover, the convolution-t distribution provides a better empirical performance than the conventional multivariate t-distribution.


[13] 2406.07286

From rank-based models with common noise to pathwise entropy solutions of SPDEs

We study the mean field limit of a rank-based model with common noise, which arises as an extension to models for the market capitalization of firms in stochastic portfolio theory. We show that, under certain conditions on the drift and diffusion coefficients, the empirical cumulative distribution function converges to the solution of a stochastic PDE. A key step in the proof, which is of independent interest, is to show that any solution to an associated martingale problem is also a pathwise entropy solution to the stochastic PDE, a notion introduced in a recent series of papers [32, 33, 19, 16, 17].


[14] 2406.07523

Change of numeraire for weak martingale transport

Change of numeraire is a classical tool in mathematical finance. Campi-Laachir-Martini established its applicability to martingale optimal transport. We note that the results of Campi-Laachir-Martini extend to the case of weak martingale transport. We apply this to shadow couplings, continuous time martingale transport problems in the framework of Huesmann-Trevisan and in particular to establish the correspondence between stretched Brownian motion with its geometric counterpart. Note: We emphasize that we learned about the geometric stretched Brownian motion gSBM (defined in PDE terms) in a presentation of Loeper \cite{Lo23} before our work on this topic started. We noticed that a change of numeraire transformation in the spirit of \cite{CaLaMa14} allows for an alternative viewpoint in the weak optimal transport framework. We make our work public following the publication of Backhoff-Loeper-Obloj's work \cite{BaLoOb24} on arxiv.org. The article \cite{BaLoOb24} derives gSBM using PDE techniques as well as through an independent probabilistic approach which is close to the one we give in the present article.