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Existence, uniqueness and positivity of solutions to the Guyon-Lekeufack path-dependent volatility model with general kernels 具有一般内核的居雍-勒库法克路径依赖波动模型解的存在性、唯一性和实在性
Pub Date : 2024-08-05 DOI: arxiv-2408.02477
Hervé AndrèsCERMICS, Benjamin JourdainCERMICS, MATHRISK
We show the existence and uniqueness of a continuous solution to apath-dependent volatility model introduced by Guyon and Lekeufack (2023) tomodel the price of an equity index and its spot volatility. The consideredmodel for the trend and activity features can be written as a StochasticVolterra Equation (SVE) with non-convolutional and non-bounded kernels as wellas non-Lipschitz coefficients. We first prove the existence and uniqueness of asolution to the SVE under integrability and regularity assumptions on the twokernels and under a condition on the second kernel weighting the past squaredreturns which ensures that the activity feature is bounded from below by apositive constant. Then, assuming in addition that the kernel weighting thepast returns is of exponential type and that an inequality relating thelogarithmic derivatives of the two kernels with respect to their secondvariables is satisfied, we show the positivity of the volatility process whichis obtained as a non-linear function of the SVE's solution. We show numericallythat the choice of an exponential kernel for the kernel weighting the pastreturns has little impact on the quality of model calibration compared to otherchoices and the inequality involving the logarithmic derivatives is satisfiedby the calibrated kernels. These results extend those of Nutz and Valdevenito(2023).
我们证明了由 Guyon 和 Lekeufack(2023 年)引入的依赖路径的波动率模型的连续解的存在性和唯一性,该模型用于模拟股票指数的价格及其现货波动率。考虑到趋势和活动特征的模型可以写成随机波动方程(SVE),具有非演化和非边界核以及非 Lipschitz 系数。我们首先证明了在两个核的可整性和正则性假设下,以及在第二个核加权过去收益平方的条件下,SVE 解的存在性和唯一性。然后,再假定加权过去收益的核是指数型的,并且满足两个核关于其次变量的对数导数的不等式,我们证明了波动率过程的实在性,该过程是作为 SVE 解的非线性函数得到的。我们从数值上证明,与其他选择相比,为过去收益加权的核选择指数核对模型校准的质量影响很小,并且校准后的核满足涉及对数导数的不等式。这些结果扩展了 Nutz 和 Valdevenito(2023 年)的研究。
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引用次数: 0
KAN based Autoencoders for Factor Models 基于 KAN 的因子模型自动编码器
Pub Date : 2024-08-04 DOI: arxiv-2408.02694
Tianqi Wang, Shubham Singh
Inspired by recent advances in Kolmogorov-Arnold Networks (KANs), weintroduce a novel approach to latent factor conditional asset pricing models.While previous machine learning applications in asset pricing havepredominantly used Multilayer Perceptrons with ReLU activation functions tomodel latent factor exposures, our method introduces a KAN-based autoencoderwhich surpasses MLP models in both accuracy and interpretability. Our modeloffers enhanced flexibility in approximating exposures as nonlinear functionsof asset characteristics, while simultaneously providing users with anintuitive framework for interpreting latent factors. Empirical backtestingdemonstrates our model's superior ability to explain cross-sectional riskexposures. Moreover, long-short portfolios constructed using our model'spredictions achieve higher Sharpe ratios, highlighting its practical value ininvestment management.
受科尔莫哥洛夫-阿诺德网络(KANs)最新进展的启发,我们为潜在因素条件资产定价模型引入了一种新方法。虽然以前在资产定价领域的机器学习应用主要使用带有 ReLU 激活函数的多层感知器对潜在因素暴露进行建模,但我们的方法引入了基于 KAN 的自动编码器,在准确性和可解释性方面都超越了 MLP 模型。我们的模型在将暴露近似为资产特征的非线性函数方面提供了更大的灵活性,同时还为用户提供了解释潜在因子的直观框架。实证回溯测试证明了我们的模型在解释横截面风险敞口方面的卓越能力。此外,利用我们的模型预测构建的多空投资组合获得了更高的夏普比率,凸显了其在投资管理中的实用价值。
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引用次数: 0
CVA Sensitivities, Hedging and Risk CVA 敏感性、套期保值和风险
Pub Date : 2024-07-26 DOI: arxiv-2407.18583
Stéphane CrépeyUFR Mathématiques UPCité, Botao LiLPSM, Hoang NguyenIES, LPSM, Bouazza Saadeddine
We present a unified framework for computing CVA sensitivities, hedging theCVA, and assessing CVA risk, using probabilistic machine learning meant asrefined regression tools on simulated data, validatable by low-cost companionMonte Carlo procedures. Various notions of sensitivities are introduced andbenchmarked numerically. We identify the sensitivities representing the bestpractical trade-offs in downstream tasks including CVA hedging and riskassessment.
我们提出了一个计算 CVA 敏感度、对冲 CVA 和评估 CVA 风险的统一框架,使用概率机器学习作为模拟数据上的精炼回归工具,并可通过低成本的配套蒙特卡罗程序进行验证。我们引入了各种敏感性概念,并对其进行了数值基准测试。我们确定了代表下游任务(包括 CVA 对冲和风险评估)中最佳实用权衡的敏感性。
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引用次数: 0
High order approximations of the log-Heston process semigroup 对数-赫斯顿过程半群的高阶近似值
Pub Date : 2024-07-24 DOI: arxiv-2407.17151
Aurélien Alfonsi, Edoardo Lombardo
We present weak approximations schemes of any order for the Heston model thatare obtained by using the method developed by Alfonsi and Bally (2021). Thismethod consists in combining approximation schemes calculated on differentrandom grids to increase the order of convergence. We apply this method witheither the Ninomiya-Victoir scheme (2008) or a second-order scheme that samplesexactly the volatility component, and we show rigorously that we can achievethen any order of convergence. We give numerical illustrations on financialexamples that validate the theoretical order of convergence, and present alsopromising numerical results for the multifactor/rough Heston model.
我们介绍了通过使用 Alfonsi 和 Bally(2021 年)开发的方法获得的 Heston 模型的任意阶弱近似方案。这种方法是将在不同随机网格上计算的近似方案结合起来,以提高收敛阶数。我们将此方法与 Ninomiya-Victoir 方案(2008 年)或精确采样波动成分的二阶方案结合使用,并严格证明我们可以达到任何收敛阶次。我们给出了金融实例的数值说明,验证了理论上的收敛阶次,并给出了多因素/透彻海斯顿模型的令人振奋的数值结果。
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引用次数: 0
Alleviating Non-identifiability: a High-fidelity Calibration Objective for Financial Market Simulation with Multivariate Time Series Data 缓解不可识别性:利用多变量时间序列数据进行金融市场模拟的高保真校准目标
Pub Date : 2024-07-23 DOI: arxiv-2407.16566
Chenkai Wang, Junji Ren, Ke Tang, Peng Yang
The non-identifiability issue has been frequently reported in the socialsimulation works, where different parameters of an agent-based simulation modelyield indistinguishable simulated time series data under certain discrepancymetrics. This issue largely undermines the simulation fidelity yet lacksdedicated investigations. This paper theoretically analyzes that incorporatingmultiple time series data features in the model calibration phase can alleviatethe non-identifiability exponentially with the increasing number of features.To implement this theoretical finding, a maximization-based aggregationfunction is applied to existing discrepancy metrics to form a new calibrationobjective function. For verification, the financial market simulation, atypical and complex social simulation task, is considered. Empirical studies onboth synthetic and real market data witness the significant improvements inalleviating the non-identifiability with much higher simulation fidelity of thechosen agent-based simulation model. Importantly, as a model-agnostic method,it achieves the first successful simulation of the high-frequency market atseconds level. Hence, this work is expected to provide not only a rigorousunderstanding of non-identifiability in social simulation, but a high-fidelitycalibration objective function for financial market simulations.
非可识别性问题在社会模拟研究中屡见报端,即在某些差异度量条件下,基于代理的模拟模式的不同参数会产生不可区分的模拟时间序列数据。这一问题在很大程度上影响了仿真的真实性,但却缺乏专门的研究。本文从理论上分析了在模型校准阶段加入多个时间序列数据特征,可以随着特征数量的增加以指数形式缓解不可识别性。为了进行验证,我们考虑了金融市场模拟这一非典型的复杂社会模拟任务。对合成和真实市场数据的实证研究证明,所选择的基于代理的仿真模型具有更高的仿真保真度,在缓解不可识别性方面取得了显著改善。重要的是,作为一种与模型无关的方法,它首次成功模拟了秒级的高频市场。因此,这项工作不仅有望为社会仿真中的非可识别性提供严谨的理解,而且有望为金融市场仿真提供高保真度的校准目标函数。
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引用次数: 0
Calibrating the Heston Model with Deep Differential Networks 用深度差分网络校准赫斯顿模型
Pub Date : 2024-07-22 DOI: arxiv-2407.15536
Chen Zhang, Giovanni Amici, Marco Morandotti
We propose a gradient-based deep learning framework to calibrate the Hestonoption pricing model (Heston, 1993). Our neural network, henceforth deepdifferential network (DDN), learns both the Heston pricing formula forplain-vanilla options and the partial derivatives with respect to the modelparameters. The price sensitivities estimated by the DDN are not subject to thenumerical issues that can be encountered in computing the gradient of theHeston pricing function. Thus, our network is an excellent pricing engine forfast gradient-based calibrations. Extensive tests on selected equity marketsshow that the DDN significantly outperforms non-differential feedforward neuralnetworks in terms of calibration accuracy. In addition, it dramatically reducesthe computational time with respect to global optimizers that do not usegradient information.
我们提出了一种基于梯度的深度学习框架来校准海斯顿期权定价模型(海斯顿,1993 年)。我们的神经网络(以下简称为深度微分网络(DDN))既能学习普通香草期权的海斯顿定价公式,也能学习模型参数的部分导数。DDN 估算的价格敏感性不受计算海斯顿定价函数梯度时可能遇到的数值问题的影响。因此,我们的网络是基于梯度校准的快速定价引擎。对选定股票市场的广泛测试表明,DDN 在校准精度方面明显优于非差分前馈神经网络。此外,与不使用梯度信息的全局优化器相比,它还大大减少了计算时间。
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引用次数: 0
Explainable AI in Request-for-Quote 询价中的可解释人工智能
Pub Date : 2024-07-21 DOI: arxiv-2407.15038
Qiqin Zhou
In the contemporary financial landscape, accurately predicting theprobability of filling a Request-For-Quote (RFQ) is crucial for improvingmarket efficiency for less liquid asset classes. This paper explores theapplication of explainable AI (XAI) models to forecast the likelihood of RFQfulfillment. By leveraging advanced algorithms including Logistic Regression,Random Forest, XGBoost and Bayesian Neural Tree, we are able to improve theaccuracy of RFQ fill rate predictions and generate the most efficient quoteprice for market makers. XAI serves as a robust and transparent tool for marketparticipants to navigate the complexities of RFQs with greater precision.
在当代金融领域,准确预测询价(RFQ)成交的可能性对于提高流动性较低的资产类别的市场效率至关重要。本文探讨了如何应用可解释人工智能(XAI)模型来预测询价成功的可能性。通过利用逻辑回归、随机森林、XGBoost 和贝叶斯神经树等先进算法,我们能够提高 RFQ 满足率预测的准确性,并为做市商生成最有效的报价。XAI 是一款强大而透明的工具,可帮助市场参与者更准确地驾驭复杂的 RFQ。
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引用次数: 0
Towards A Post-Quantum Cryptography in Blockchain I: Basic Review on Theoretical Cryptography and Quantum Information Theory 迈向区块链中的后量子密码学 I:理论密码学和量子信息论基本回顾
Pub Date : 2024-07-19 DOI: arxiv-2407.18966
Tatsuru Kikuchi
Recently, the invention of quantum computers was so revolutionary that theybring transformative challenges in a variety of fields, especially for thetraditional cryptographic blockchain, and it may become a real thread for mostof the cryptocurrencies in the market. That is, it becomes inevitable toconsider to implement a post-quantum cryptography, which is also referred to asquantum-resistant cryptography, for attaining quantum resistance inblockchains.
最近,量子计算机的发明是如此具有革命性,它给各个领域带来了变革性的挑战,尤其是对于传统的加密区块链来说,它可能会成为市场上大多数加密货币的真正主线。也就是说,为了实现区块链的量子抗性,考虑实现后量子加密技术(也称为量子抗性加密技术)成为必然。
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引用次数: 0
Leveraging Machine Learning for High-Dimensional Option Pricing within the Uncertain Volatility Model 在不确定波动率模型中利用机器学习进行高维期权定价
Pub Date : 2024-07-18 DOI: arxiv-2407.13213
Ludovic Goudenege, Andrea Molent, Antonino Zanette
This paper explores the application of Machine Learning techniques forpricing high-dimensional options within the framework of the UncertainVolatility Model (UVM). The UVM is a robust framework that accounts for theinherent unpredictability of market volatility by setting upper and lowerbounds on volatility and the correlation among underlying assets. By leveraginghistorical data and extreme values of estimated volatilities and correlations,the model establishes a confidence interval for future volatility andcorrelations, thus providing a more realistic approach to option pricing. Byintegrating advanced Machine Learning algorithms, we aim to enhance theaccuracy and efficiency of option pricing under the UVM, especially when theoption price depends on a large number of variables, such as in basket orpath-dependent options. Our approach evolves backward in time, dynamicallyselecting at each time step the most expensive volatility and correlation foreach market state. Specifically, it identifies the particular values ofvolatility and correlation that maximize the expected option value at the nexttime step. This is achieved through the use of Gaussian Process regression, thecomputation of expectations via a single step of a multidimensional tree andthe Sequential Quadratic Programming optimization algorithm. The numericalresults demonstrate that the proposed approach can significantly improve theprecision of option pricing and risk management strategies compared withmethods already in the literature, particularly in high-dimensional contexts.
本文探讨了在不确定波动率模型(UVM)框架内应用机器学习技术为高维期权定价的问题。不确定波动率模型是一个稳健的框架,它通过设置波动率的上限和下限以及标的资产之间的相关性来考虑市场波动率固有的不可预测性。通过利用历史数据和估计波动率和相关性的极端值,该模型建立了未来波动率和相关性的置信区间,从而为期权定价提供了更现实的方法。通过整合先进的机器学习算法,我们旨在提高 UVM 下期权定价的准确性和效率,尤其是当期权价格依赖于大量变量时,如一揽子期权或路径依赖期权。我们的方法在时间上向后发展,在每个时间步动态选择每个市场状态下最昂贵的波动率和相关性。具体来说,它能识别出在下一个时间步最大化期权预期价值的波动率和相关性的特定值。这是通过使用高斯过程回归、多维树的单步预期计算和顺序二次编程优化算法来实现的。数值结果表明,与文献中已有的方法相比,特别是在高维背景下,所提出的方法可以显著提高期权定价和风险管理策略的精确度。
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引用次数: 0
Temporal Representation Learning for Stock Similarities and Its Applications in Investment Management 股票相似性的时态表征学习及其在投资管理中的应用
Pub Date : 2024-07-18 DOI: arxiv-2407.13751
Yoontae Hwang, Stefan Zohren, Yongjae Lee
In the era of rapid globalization and digitalization, accurate identificationof similar stocks has become increasingly challenging due to the non-stationarynature of financial markets and the ambiguity in conventional regional andsector classifications. To address these challenges, we examine SimStock, anovel temporal self-supervised learning framework that combines techniques fromself-supervised learning (SSL) and temporal domain generalization to learnrobust and informative representations of financial time series data. Theprimary focus of our study is to understand the similarities between stocksfrom a broader perspective, considering the complex dynamics of the globalfinancial landscape. We conduct extensive experiments on four real-worlddatasets with thousands of stocks and demonstrate the effectiveness of SimStockin finding similar stocks, outperforming existing methods. The practicalutility of SimStock is showcased through its application to various investmentstrategies, such as pairs trading, index tracking, and portfolio optimization,where it leads to superior performance compared to conventional methods. Ourfindings empirically examine the potential of data-driven approach to enhanceinvestment decision-making and risk management practices by leveraging thepower of temporal self-supervised learning in the face of the ever-changingglobal financial landscape.
在快速全球化和数字化的时代,由于金融市场的非稳态性以及传统地区和行业分类的模糊性,准确识别相似股票变得越来越具有挑战性。为了应对这些挑战,我们对 SimStock 进行了研究,这是一种高级时态自监督学习框架,它结合了自监督学习(SSL)和时态域泛化技术,可以学习金融时间序列数据的稳健且信息丰富的表征。我们研究的主要重点是从更广阔的视角来理解股票之间的相似性,同时考虑到全球金融格局的复杂动态。我们在四个包含数千只股票的真实世界数据集上进行了大量实验,证明了 SimStock 在发现相似股票方面的有效性,其表现优于现有方法。通过将 SimStock 应用于各种投资策略(如配对交易、指数跟踪和投资组合优化),我们展示了 SimStock 的实用性,与传统方法相比,SimStock 的性能更为卓越。面对瞬息万变的全球金融形势,我们的研究结果通过实证检验了数据驱动方法的潜力,即利用时态自监督学习的能力来增强投资决策和风险管理实践。
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引用次数: 0
期刊
arXiv - QuantFin - Computational Finance
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