Quantitative Finance

Kwon, Sohyeon; Lee, Yongjae

doi: 10.48550/arxiv.2410.09850pmid: N/A

Abstract:In the financial sector, a sophisticated financial time series simulator is essential for evaluating financial products and investment strategies. Traditional back-testing methods have mainly relied on historical data-driven approaches or mathematical model-driven approaches, such as various stochastic processes. However, in the current era of AI, data-driven approaches, where models learn the intrinsic characteristics of data directly, have emerged as promising techniques. Generative Adversarial Networks (GANs) have surfaced as promising generative models, capturing data distributions through adversarial learning. Financial time series, characterized 'stylized facts' such as random walks, mean-reverting patterns, unexpected jumps, and time-varying volatility, present significant challenges for deep neural networks to learn their intrinsic characteristics. This study examines the ability of GANs to learn diverse and complex temporal patterns (i.e., stylized facts) of both univariate and multivariate financial time series. Our extensive experiments revealed that GANs can capture various stylized facts of financial time series, but their performance varies significantly depending on the choice of generator architecture. This suggests that naively applying GANs might not effectively capture the intricate characteristics inherent in financial time series, highlighting the importance of carefully considering and validating the modeling choices.

Fleck, Andrew; Furman, Edward; Shen, Yang

doi: 10.48550/arxiv.2410.14985pmid: N/A

Abstract:Nowadays insurers have to account for potentially complex dependence between risks. In the field of loss reserving, there are many parametric and non-parametric models attempting to capture dependence between business lines. One common approach has been to use additive background risk models (ABRMs) which provide rich and interpretable dependence structures via a common shock model. Unfortunately, ABRMs are often restrictive. Models that capture necessary features may have impractical to estimate parameters. For example models without a closed-form likelihood function for lack of a probability density function (e.g. some Tweedie, Stable Distributions, etc). We apply a modification of the continuous generalised method of moments (CGMM) of [Carrasco and Florens, 2000] which delivers comparable estimators to the MLE to loss reserving. We examine models such as the one proposed by [Avanzi et al., 2016] and a related but novel one derived from the stable family of distributions. Our CGMM method of estimation provides conventional non-Bayesian estimates in the case where MLEs are impractical.

D'Auria, Bernardo; Escudero, Carlos

doi: 10.48550/arxiv.2410.16010pmid: N/A

Abstract:We study the anticipating version of the classical portfolio optimization problem in a financial market with the presence of a trader who possesses privileged information about the future (insider information), but who is also subjected to a delay in the information flow about the market conditions; hence this trader possesses an asymmetric information with respect to the traditional one. We analyze it via the Russo-Vallois forward stochastic integral, i. e. using anticipating stochastic calculus, along with a white noise approach. We explicitly compute the optimal portfolios that maximize the expected logarithmic utility assuming different classical financial models: Black-Scholes-Merton, Heston, Vasicek. Similar results hold for other well-known models, such as the Hull-White and the Cox-Ingersoll-Ross ones. Our comparison between the performance of the traditional trader and the insider, although only asymmetrically informed, reveals that the privileged information overcompensates the delay in all cases, provided only one information flow is delayed. However, when two information flows are delayed, a competition between future information and delay magnitude enters into play, implying that the best performance depends on the parameter values. This, in turn, allows us to value future information in terms of time, and not only utility.

Gnabeyeu, Emmanuel; Karkar, Omar; Idboufous, Imad

doi: 10.48550/arxiv.2410.11789pmid: N/A

Abstract:The volatility fitting is one of the core problems in the equity derivatives business. Through a set of deterministic rules, the degrees of freedom in the implied volatility surface encoding (parametrization, density, diffusion) are defined. Whilst very effective, this approach widespread in the industry is not natively tailored to learn from shifts in market regimes and discover unsuspected optimal behaviors. In this paper, we change the classical paradigm and apply the latest advances in Deep Reinforcement Learning(DRL) to solve the fitting problem. In particular, we show that variants of Deep Deterministic Policy Gradient (DDPG) and Soft Actor Critic (SAC) can achieve at least as good as standard fitting algorithms. Furthermore, we explain why the reinforcement learning framework is appropriate to handle complex objective functions and is natively adapted for online learning.

Cai, Jun; Jiao, Zhanyi; Mao, Tiantian

doi: 10.48550/arxiv.2410.01732pmid: N/A

Abstract:The expected regret and target semi-variance are two of the most important risk measures for downside risk. When the distribution of a loss is uncertain, and only partial information of the loss is known, their worst-case values play important roles in robust risk management for finance, insurance, and many other fields. Jagannathan (1977) derived the worst-case expected regrets when only the mean and variance of a loss are known and the loss is arbitrary, symmetric, or non-negative. While Chen et al. (2011) obtained the worst-case target semi-variances under similar conditions but focusing on arbitrary losses. In this paper, we first complement the study of Chen et al. (2011) on the worst-case target semi-variances and derive the closed-form expressions for the worst-case target semi-variance when only the mean and variance of a loss are known and the loss is symmetric or non-negative. Then, we investigate worst-case target semi-variances over uncertainty sets that represent undesirable scenarios faced by an investors. Our methods for deriving these worst-case values are different from those used in Jagannathan (1977) and Chen et al. (2011). As applications of the results derived in this paper, we propose robust portfolio selection methods that minimize the worst-case target semi-variance of a portfolio loss over different uncertainty sets. To explore the insights of our robust portfolio selection methods, we conduct numerical experiments with real financial data and compare our portfolio selection methods with several existing portfolio selection models related to the models proposed in this paper.

Gawronsky, Marcus; Huang, Chun-Sung

doi: 10.48550/arxiv.2410.23447pmid: N/A

Abstract:This paper introduces a novel approach to financial risk analysis that does not rely on traditional price and market data, instead using market news to model assets as distributions over a metric space of risk factors. By representing asset returns as integrals over the scalar field of these risk factors, we derive the covariance structure between asset returns. Utilizing encoder-only language models to embed this news data, we explore the relationships between asset return distributions through the concept of Energy Distance, establishing connections between distributional differences and excess returns co-movements. This data-agnostic approach provides new insights into portfolio diversification, risk management, and the construction of hedging strategies. Our findings have significant implications for both theoretical finance and practical risk management, offering a more robust framework for modelling complex financial systems without depending on conventional market data.

Papaioannou, Panayotis G.; Papaioannou, George P.; Evangelidis, George; Gavalakis, George

doi: 10.48550/arxiv.2410.07224pmid: N/A

Abstract:We investigate the impact of several critical events associated with the Russo Ukrainian war, started officially on 24 February 2022 with the Russian invasion of Ukraine, on ten European electricity markets, two natural gas markets (the European reference trading hub TTF and N.Y. NGNMX market) and how these markets interact to each other and with USDRUB exchange rate, a financial market. We analyze the reactions of these markets, manifested as breakpoints attributed to these critical events, and their interaction, by using a set of three tools that can shed light on different aspects of this complex situation. We combine the concepts of market efficiency, measured by quantifying the Efficient market hypothesis (EMH) via rolling Hurst exponent, with structural breakpoints occurred in the time series of gas, electricity and financial markets, the detection of which is possible by using a Bayesian ensemble approach, the Bayesian Estimator of Abrupt change, Seasonal change and Trend (BEAST), a powerful tool that can effectively detect structural breakpoints, trends, seasonalities and sudden abrupt changes in time series. The results show that the analyzed markets have exhibited different modes of reactions to the critical events, both in respect of number, nature, and time of occurrence (leading, lagging, concurrent with dates of critical events) of breakpoints as well as of the dynamic behavior of their trend components.

De, Anushka

doi: 10.48550/arxiv.2410.07228pmid: N/A

Abstract:The COVID-19 pandemic struck education system around the globe and initiated an immediate and complete lockdown of all the educational institutions, to maintain social distancing. CRY (Child Rights and You) in collaboration with RILM (Rotary India Literacy Mission) initiated a project to assess the learning abilities of 4000 children across four states: Jammu & Kashmir, Jharkhand, Manipur and West Bengal. Every child was provided with the books of appropriate class according to their age in order to test their competency in reading and basic calculation as well and thereafter the compatible class was determined. The assessments were carried over 3 quarters in 4 subjects: oral assessments in 1st Language, 2nd Language and Mathematics and a writing assessment and a binary variable for improvement or no improvement (1/0) was provided. This paper suggests a measure which gives a unique score for improvement level of students with varied class lag since it will not be a desirable idea to grade the students with varied class lags on the same basis. This paper also investigates and evaluates the progression of student performance over the 3 quarters, suggests the use of a comprehensive score measure for summarising the inter-quarter performance. The analysis of progression has been carried out by gender and state level for male-female and inter state comparison respectively.

Criens, David; Urusov, Mikhail

doi: 10.48550/arxiv.2410.09789pmid: N/A

Abstract:In a seminal paper, F. Delbaen and W. Schachermayer proved that the classical NA ("no arbitrage") condition implies the existence of an "absolutely continuous local martingale measure" (ACLMM). It is known that in general the existence of an ACLMM alone is not sufficient for NA. In this paper we investigate how close these notions are for single asset general diffusion market models. We show that NA is equivalent to the existence of an ACLMM plus a mild regularity condition on the scale function and the absence of reflecting boundaries. For infinite time horizon scenarios, the regularity assumption and the requirement on the boundaries can be dropped, showing equivalence between NA and the existence of an ACLMM. By means of counterexamples, we show that our characterization of NA for finite time horizons is sharp in the sense that neither the regularity condition on the scale function nor the absence of reflecting boundaries can be dropped.

Mirmominov, Ruslan; Wiesel, Johannes

doi: 10.48550/arxiv.2410.23927pmid: N/A

Abstract:We consider multiperiod stochastic control problems with non-parametric uncertainty on the underlying probabilistic model. We derive a new metric on the space of probability measures, called the adapted $(p, \infty)$--Wasserstein distance $\mathcal{AW}_p^\infty$ with the following properties: (1) the adapted $(p, \infty)$--Wasserstein distance generates a topology that guarantees continuity of stochastic control problems and (2) the corresponding $\mathcal{AW}_p^\infty$-distributionally robust optimization (DRO) problem can be computed via a dynamic programming principle involving one-step Wasserstein-DRO problems. If the cost function is semi-separable, then we further show that a minimax theorem holds, even though balls with respect to $\mathcal{AW}_p^\infty$ are neither convex nor compact in general. We also derive first-order sensitivity results.