Market fluctuations caused by overtrading are important components of systemic market risk. This study examines the effect of investor sentiment on intraday overtrading activities in the Chinese A-share market. Employing high-frequency sentiment indices inferred from social media posts on the Eastmoney forum Guba, the research focuses on constituents of the CSI 300 and CSI 500 indices over a period from 01/01/2018, to 12/30/2022. The empirical analysis indicates that investor sentiment exerts a significantly positive impact on intraday overtrading, with the influence being more pronounced among institutional investors relative to individual traders. Moreover, sentiment-driven overtrading is found to be more prevalent during bull markets as opposed to bear markets. Additionally, the effect of sentiment on overtrading is observed to be more pronounced among individual investors in large-cap stocks compared to small- and mid-cap stocks.
过度交易引起的市场波动是系统性市场风险的重要组成部分。本研究探讨了投资者情绪对中国 A 股市场当日过度交易活动的影响。研究采用从东财论坛Guba上的社交媒体帖子中推断出的高频情绪指数，重点研究了2018年1月1日至2022年12月30日期间沪深300指数和中证500指数的成分股。实证分析表明，投资者情绪对日内过度交易有显著的正向影响，相对于个人交易者，这种影响在机构投资者中更为明显。此外，研究还发现情绪驱动的过度交易在牛市中比熊市中更为普遍。此外，与中小盘股相比，情绪对过度交易的影响在大盘股的个人投资者中更为明显。
{"title":"Internet sentiment exacerbates intraday overtrading, evidence from A-Share market","authors":"Peng Yifeng","doi":"arxiv-2404.12001","DOIUrl":"https://doi.org/arxiv-2404.12001","url":null,"abstract":"Market fluctuations caused by overtrading are important components of\u0000systemic market risk. This study examines the effect of investor sentiment on\u0000intraday overtrading activities in the Chinese A-share market. Employing\u0000high-frequency sentiment indices inferred from social media posts on the\u0000Eastmoney forum Guba, the research focuses on constituents of the CSI 300 and\u0000CSI 500 indices over a period from 01/01/2018, to 12/30/2022. The empirical\u0000analysis indicates that investor sentiment exerts a significantly positive\u0000impact on intraday overtrading, with the influence being more pronounced among\u0000institutional investors relative to individual traders. Moreover,\u0000sentiment-driven overtrading is found to be more prevalent during bull markets\u0000as opposed to bear markets. Additionally, the effect of sentiment on\u0000overtrading is observed to be more pronounced among individual investors in\u0000large-cap stocks compared to small- and mid-cap stocks.","PeriodicalId":501294,"journal":{"name":"arXiv - QuantFin - Computational Finance","volume":"50 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140623205","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Francisco Gómez Casanova, Álvaro Leitao, Fernando de Lope Contreras, Carlos Vázquez
This paper addresses the problem of pricing involved financial derivatives by means of advanced of deep learning techniques. More precisely, we smartly combine several sophisticated neural network-based concepts like differential machine learning, Monte Carlo simulation-like training samples and joint learning to come up with an efficient numerical solution. The application of the latter development represents a novelty in the context of computational finance. We also propose a novel design of interdependent neural networks to price early-exercise products, in this case, Bermudan swaptions. The improvements in efficiency and accuracy provided by the here proposed approach is widely illustrated throughout a range of numerical experiments. Moreover, this novel methodology can be extended to the pricing of other financial derivatives.
{"title":"Deep Joint Learning valuation of Bermudan Swaptions","authors":"Francisco Gómez Casanova, Álvaro Leitao, Fernando de Lope Contreras, Carlos Vázquez","doi":"arxiv-2404.11257","DOIUrl":"https://doi.org/arxiv-2404.11257","url":null,"abstract":"This paper addresses the problem of pricing involved financial derivatives by\u0000means of advanced of deep learning techniques. More precisely, we smartly\u0000combine several sophisticated neural network-based concepts like differential\u0000machine learning, Monte Carlo simulation-like training samples and joint\u0000learning to come up with an efficient numerical solution. The application of\u0000the latter development represents a novelty in the context of computational\u0000finance. We also propose a novel design of interdependent neural networks to\u0000price early-exercise products, in this case, Bermudan swaptions. The\u0000improvements in efficiency and accuracy provided by the here proposed approach\u0000is widely illustrated throughout a range of numerical experiments. Moreover,\u0000this novel methodology can be extended to the pricing of other financial\u0000derivatives.","PeriodicalId":501294,"journal":{"name":"arXiv - QuantFin - Computational Finance","volume":"12 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140614879","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We consider the Ornstein-Uhlenbeck (OU) process, a stochastic process widely used in finance, physics, and biology. Parameter estimation of the OU process is a challenging problem. Thus, we review traditional tracking methods and compare them with novel applications of deep learning to estimate the parameters of the OU process. We use a multi-layer perceptron to estimate the parameters of the OU process and compare its performance with traditional parameter estimation methods, such as the Kalman filter and maximum likelihood estimation. We find that the multi-layer perceptron can accurately estimate the parameters of the OU process given a large dataset of observed trajectories; however, traditional parameter estimation methods may be more suitable for smaller datasets.
我们考虑的是奥恩斯坦-乌伦贝克（OU）过程，这是一种广泛应用于金融、物理和生物学的随机过程。OU 过程的参数估计是一个具有挑战性的问题。因此，我们回顾了传统的跟踪方法，并将它们与深度学习在估计 OU 过程参数方面的新应用进行了比较。我们使用多层感知器来估计 OU 过程的参数，并将其性能与卡尔曼滤波和最大似然估计等传统参数估计方法进行比较。我们发现，在观测到大量轨迹数据集的情况下，多层感知器可以准确地估计OU过程的参数；然而，传统的参数估计方法可能更适用于较小的数据集。
{"title":"A Comparison of Traditional and Deep Learning Methods for Parameter Estimation of the Ornstein-Uhlenbeck Process","authors":"Jacob Fein-Ashley","doi":"arxiv-2404.11526","DOIUrl":"https://doi.org/arxiv-2404.11526","url":null,"abstract":"We consider the Ornstein-Uhlenbeck (OU) process, a stochastic process widely\u0000used in finance, physics, and biology. Parameter estimation of the OU process\u0000is a challenging problem. Thus, we review traditional tracking methods and\u0000compare them with novel applications of deep learning to estimate the\u0000parameters of the OU process. We use a multi-layer perceptron to estimate the\u0000parameters of the OU process and compare its performance with traditional\u0000parameter estimation methods, such as the Kalman filter and maximum likelihood\u0000estimation. We find that the multi-layer perceptron can accurately estimate the\u0000parameters of the OU process given a large dataset of observed trajectories;\u0000however, traditional parameter estimation methods may be more suitable for\u0000smaller datasets.","PeriodicalId":501294,"journal":{"name":"arXiv - QuantFin - Computational Finance","volume":"68 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140608371","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A long-standing issue in mathematical finance is the speed-up of pricing options, especially multi-asset options. A recent study has proposed to use tensor train learning algorithms to speed up Fourier transform (FT)-based option pricing, utilizing the ability of tensor networks to compress high-dimensional tensors. Another usage of the tensor network is to compress functions, including their parameter dependence. In this study, we propose a pricing method, where, by a tensor learning algorithm, we build tensor trains that approximate functions appearing in FT-based option pricing with their parameter dependence and efficiently calculate the option price for the varying input parameters. As a benchmark test, we run the proposed method to price a multi-asset option for the various values of volatilities and present asset prices. We show that, in the tested cases involving up to about 10 assets, the proposed method is comparable to or outperforms Monte Carlo simulation with $10^5$ paths in terms of computational complexity, keeping the comparable accuracy.
数学金融学中一个长期存在的问题是加快期权定价，尤其是多资产期权的定价。最近的一项研究提出，利用张量网络压缩高维张量的能力，使用张量训练学习算法来加速基于傅立叶变换（FT）的期权定价。张量网络的另一个用途是压缩函数，包括其参数依赖性。在本研究中，我们提出了一种定价方法，即通过张量学习算法，建立张量训练，以近似基于 FT 的期权定价中出现的函数及其参数依赖性，并有效计算不同输入参数下的期权价格。作为基准测试，我们使用所提出的方法对不同波动率值和资产现价的多资产期权进行了定价。结果表明，在涉及多达 10 种资产的测试案例中，所提出的方法在计算复杂度方面与采用 10^5$ 路径的蒙特卡罗模拟方法相当，甚至优于后者，同时保持了相当的准确性。
{"title":"Learning tensor networks with parameter dependence for Fourier-based option pricing","authors":"Rihito Sakurai, Haruto Takahashi, Koichi Miyamoto","doi":"arxiv-2405.00701","DOIUrl":"https://doi.org/arxiv-2405.00701","url":null,"abstract":"A long-standing issue in mathematical finance is the speed-up of pricing\u0000options, especially multi-asset options. A recent study has proposed to use\u0000tensor train learning algorithms to speed up Fourier transform (FT)-based\u0000option pricing, utilizing the ability of tensor networks to compress\u0000high-dimensional tensors. Another usage of the tensor network is to compress\u0000functions, including their parameter dependence. In this study, we propose a\u0000pricing method, where, by a tensor learning algorithm, we build tensor trains\u0000that approximate functions appearing in FT-based option pricing with their\u0000parameter dependence and efficiently calculate the option price for the varying\u0000input parameters. As a benchmark test, we run the proposed method to price a\u0000multi-asset option for the various values of volatilities and present asset\u0000prices. We show that, in the tested cases involving up to about 10 assets, the\u0000proposed method is comparable to or outperforms Monte Carlo simulation with\u0000$10^5$ paths in terms of computational complexity, keeping the comparable\u0000accuracy.","PeriodicalId":501294,"journal":{"name":"arXiv - QuantFin - Computational Finance","volume":"2 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140829429","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Large language models (LLMs) are now widely used in various fields, including finance. However, Japanese financial-specific LLMs have not been proposed yet. Hence, this study aims to construct a Japanese financial-specific LLM through continual pre-training. Before tuning, we constructed Japanese financial-focused datasets for continual pre-training. As a base model, we employed a Japanese LLM that achieved state-of-the-art performance on Japanese financial benchmarks among the 10-billion-class parameter models. After continual pre-training using the datasets and the base model, the tuned model performed better than the original model on the Japanese financial benchmarks. Moreover, the outputs comparison results reveal that the tuned model's outputs tend to be better than the original model's outputs in terms of the quality and length of the answers. These findings indicate that domain-specific continual pre-training is also effective for LLMs. The tuned model is publicly available on Hugging Face.
大语言模型（LLM）目前已广泛应用于各个领域，包括金融领域。因此，本研究旨在通过持续的预训练构建日语金融专用 LLM。在调整之前，我们构建了以日本金融为重点的数据集，用于持续预训练。作为基础模型，我们使用了一个日本 LLM，该 LLM 在日本金融基准测试中取得了百亿级参数模型中最先进的性能。在使用数据集和基础模型进行持续预训练后，调整后的模型在日本金融基准测试中的表现优于原始模型。此外，输出比较结果表明，就答案的质量和长度而言，调整后模型的输出最终优于原始模型的输出。这些结果表明，针对特定领域的持续预训练对 LLM 也很有效。调整后的模型可在 "Hugging Face "网站上公开获取。
{"title":"Construction of Domain-specified Japanese Large Language Model for Finance through Continual Pre-training","authors":"Masanori Hirano, Kentaro Imajo","doi":"arxiv-2404.10555","DOIUrl":"https://doi.org/arxiv-2404.10555","url":null,"abstract":"Large language models (LLMs) are now widely used in various fields, including\u0000finance. However, Japanese financial-specific LLMs have not been proposed yet.\u0000Hence, this study aims to construct a Japanese financial-specific LLM through\u0000continual pre-training. Before tuning, we constructed Japanese\u0000financial-focused datasets for continual pre-training. As a base model, we\u0000employed a Japanese LLM that achieved state-of-the-art performance on Japanese\u0000financial benchmarks among the 10-billion-class parameter models. After\u0000continual pre-training using the datasets and the base model, the tuned model\u0000performed better than the original model on the Japanese financial benchmarks.\u0000Moreover, the outputs comparison results reveal that the tuned model's outputs\u0000tend to be better than the original model's outputs in terms of the quality and\u0000length of the answers. These findings indicate that domain-specific continual\u0000pre-training is also effective for LLMs. The tuned model is publicly available\u0000on Hugging Face.","PeriodicalId":501294,"journal":{"name":"arXiv - QuantFin - Computational Finance","volume":"214 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140614793","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
On the surface, behavioural science and physics seem to be two disparate fields of research. However, a closer examination of problems solved by them reveals that they are uniquely related to one another. Exemplified by the theories of quantum mind, cognition and decision-making, this unique relationship serves as the topic of this chapter. Surveying the current academic journal papers and scholarly monographs, we present an alternative vision of the role of quantum mechanics in the modern studies of human perception, behaviour and decision-making. To that end, we mostly aim to answer the 'how' question, deliberately avoiding complex mathematical concepts but developing a technically simple computational code that the readers can modify to design their own quantum-inspired models. We also present several practical examples of the application of the computation code and outline several plausible scenarios, where quantum models based on the proposed do-it-yourself model kit can help understand the differences between the behaviour of individuals and social groups.
{"title":"Quantum Mechanics of Human Perception, Behaviour and Decision-Making: A Do-It-Yourself Model Kit for Modelling Optical Illusions and Opinion Formation in Social Networks","authors":"Ivan S. Maksymov","doi":"arxiv-2404.10554","DOIUrl":"https://doi.org/arxiv-2404.10554","url":null,"abstract":"On the surface, behavioural science and physics seem to be two disparate\u0000fields of research. However, a closer examination of problems solved by them\u0000reveals that they are uniquely related to one another. Exemplified by the\u0000theories of quantum mind, cognition and decision-making, this unique\u0000relationship serves as the topic of this chapter. Surveying the current\u0000academic journal papers and scholarly monographs, we present an alternative\u0000vision of the role of quantum mechanics in the modern studies of human\u0000perception, behaviour and decision-making. To that end, we mostly aim to answer\u0000the 'how' question, deliberately avoiding complex mathematical concepts but\u0000developing a technically simple computational code that the readers can modify\u0000to design their own quantum-inspired models. We also present several practical\u0000examples of the application of the computation code and outline several\u0000plausible scenarios, where quantum models based on the proposed do-it-yourself\u0000model kit can help understand the differences between the behaviour of\u0000individuals and social groups.","PeriodicalId":501294,"journal":{"name":"arXiv - QuantFin - Computational Finance","volume":"16 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140614836","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Nikitas Stamatopoulos, B. David Clader, Stefan Woerner, William J. Zeng
We introduce two quantum algorithms to compute the Value at Risk (VaR) and Conditional Value at Risk (CVaR) of financial derivatives using quantum computers: the first by applying existing ideas from quantum risk analysis to derivative pricing, and the second based on a novel approach using Quantum Signal Processing (QSP). Previous work in the literature has shown that quantum advantage is possible in the context of individual derivative pricing and that advantage can be leveraged in a straightforward manner in the estimation of the VaR and CVaR. The algorithms we introduce in this work aim to provide an additional advantage by encoding the derivative price over multiple market scenarios in superposition and computing the desired values by applying appropriate transformations to the quantum system. We perform complexity and error analysis of both algorithms, and show that while the two algorithms have the same asymptotic scaling the QSP-based approach requires significantly fewer quantum resources for the same target accuracy. Additionally, by numerically simulating both quantum and classical VaR algorithms, we demonstrate that the quantum algorithm can extract additional advantage from a quantum computer compared to individual derivative pricing. Specifically, we show that under certain conditions VaR estimation can lower the latest published estimates of the logical clock rate required for quantum advantage in derivative pricing by up to $sim 30$x. In light of these results, we are encouraged that our formulation of derivative pricing in the QSP framework may be further leveraged for quantum advantage in other relevant financial applications, and that quantum computers could be harnessed more efficiently by considering problems in the financial sector at a higher level.
我们介绍了两种利用量子计算机计算金融衍生品风险值（VaR）和条件风险值（CVaR）的量子算法：第一种算法将量子风险分析的现有思想应用于衍生品定价，第二种算法基于量子信号处理（QSP）的新方法。之前的文献研究表明，量子优势在单个衍生品定价方面是可行的，并且可以直接利用量子优势来估算 VaR 和 CVaR。我们在这项工作中介绍的算法旨在通过对多个市场情景的衍生品价格进行叠加编码，并通过对量子系统应用适当的变换来计算所需的值，从而提供额外的优势。我们对这两种算法进行了复杂性和误差分析，结果表明，虽然这两种算法具有相同的渐进缩放，但基于 QSP 的方法在目标精度相同的情况下所需的量子资源要少得多。此外，通过对量子算法和经典 VaR 算法进行数值模拟，我们证明量子算法可以从量子计算机中获取比单个衍生品定价更多的优势。具体来说，我们证明了在特定条件下，VaR 估值可以将最新公布的衍生品定价中量子优势所需的逻辑时钟频率估计值降低多达 $sim 30$x。鉴于这些结果，我们感到鼓舞的是，我们在 QSP 框架中对衍生品定价的表述可能会在其他相关金融应用中进一步发挥量子优势，而且通过在更高层次上考虑金融领域的问题，可以更有效地利用量子计算机。
{"title":"Quantum Risk Analysis of Financial Derivatives","authors":"Nikitas Stamatopoulos, B. David Clader, Stefan Woerner, William J. Zeng","doi":"arxiv-2404.10088","DOIUrl":"https://doi.org/arxiv-2404.10088","url":null,"abstract":"We introduce two quantum algorithms to compute the Value at Risk (VaR) and\u0000Conditional Value at Risk (CVaR) of financial derivatives using quantum\u0000computers: the first by applying existing ideas from quantum risk analysis to\u0000derivative pricing, and the second based on a novel approach using Quantum\u0000Signal Processing (QSP). Previous work in the literature has shown that quantum\u0000advantage is possible in the context of individual derivative pricing and that\u0000advantage can be leveraged in a straightforward manner in the estimation of the\u0000VaR and CVaR. The algorithms we introduce in this work aim to provide an\u0000additional advantage by encoding the derivative price over multiple market\u0000scenarios in superposition and computing the desired values by applying\u0000appropriate transformations to the quantum system. We perform complexity and\u0000error analysis of both algorithms, and show that while the two algorithms have\u0000the same asymptotic scaling the QSP-based approach requires significantly fewer\u0000quantum resources for the same target accuracy. Additionally, by numerically\u0000simulating both quantum and classical VaR algorithms, we demonstrate that the\u0000quantum algorithm can extract additional advantage from a quantum computer\u0000compared to individual derivative pricing. Specifically, we show that under\u0000certain conditions VaR estimation can lower the latest published estimates of\u0000the logical clock rate required for quantum advantage in derivative pricing by\u0000up to $sim 30$x. In light of these results, we are encouraged that our\u0000formulation of derivative pricing in the QSP framework may be further leveraged\u0000for quantum advantage in other relevant financial applications, and that\u0000quantum computers could be harnessed more efficiently by considering problems\u0000in the financial sector at a higher level.","PeriodicalId":501294,"journal":{"name":"arXiv - QuantFin - Computational Finance","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140614876","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Derivative hedging and pricing are important and continuously studied topics in financial markets. Recently, deep hedging has been proposed as a promising approach that uses deep learning to approximate the optimal hedging strategy and can handle incomplete markets. However, deep hedging usually requires underlying asset simulations, and it is challenging to select the best model for such simulations. This study proposes a new approach using artificial market simulations for underlying asset simulations in deep hedging. Artificial market simulations can replicate the stylized facts of financial markets, and they seem to be a promising approach for deep hedging. We investigate the effectiveness of the proposed approach by comparing its results with those of the traditional approach, which uses mathematical finance models such as Brownian motion and Heston models for underlying asset simulations. The results show that the proposed approach can achieve almost the same level of performance as the traditional approach without mathematical finance models. Finally, we also reveal that the proposed approach has some limitations in terms of performance under certain conditions.
{"title":"Experimental Analysis of Deep Hedging Using Artificial Market Simulations for Underlying Asset Simulators","authors":"Masanori Hirano","doi":"arxiv-2404.09462","DOIUrl":"https://doi.org/arxiv-2404.09462","url":null,"abstract":"Derivative hedging and pricing are important and continuously studied topics\u0000in financial markets. Recently, deep hedging has been proposed as a promising\u0000approach that uses deep learning to approximate the optimal hedging strategy\u0000and can handle incomplete markets. However, deep hedging usually requires\u0000underlying asset simulations, and it is challenging to select the best model\u0000for such simulations. This study proposes a new approach using artificial\u0000market simulations for underlying asset simulations in deep hedging. Artificial\u0000market simulations can replicate the stylized facts of financial markets, and\u0000they seem to be a promising approach for deep hedging. We investigate the\u0000effectiveness of the proposed approach by comparing its results with those of\u0000the traditional approach, which uses mathematical finance models such as\u0000Brownian motion and Heston models for underlying asset simulations. The results\u0000show that the proposed approach can achieve almost the same level of\u0000performance as the traditional approach without mathematical finance models.\u0000Finally, we also reveal that the proposed approach has some limitations in\u0000terms of performance under certain conditions.","PeriodicalId":501294,"journal":{"name":"arXiv - QuantFin - Computational Finance","volume":"26 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140566004","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Enhancing the existing solution for pricing of fixed income instruments within Black-Karasinski model structure, with neural network at various parameterisation points to demonstrate that the method is able to achieve superior outcomes for multiple calibrations across extended projection horizons.
{"title":"Enhancing path-integral approximation for non-linear diffusion with neural network","authors":"Anna Knezevic","doi":"arxiv-2404.08903","DOIUrl":"https://doi.org/arxiv-2404.08903","url":null,"abstract":"Enhancing the existing solution for pricing of fixed income instruments\u0000within Black-Karasinski model structure, with neural network at various\u0000parameterisation points to demonstrate that the method is able to achieve\u0000superior outcomes for multiple calibrations across extended projection\u0000horizons.","PeriodicalId":501294,"journal":{"name":"arXiv - QuantFin - Computational Finance","volume":"118 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140565601","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this work, we propose a novel backward differential deep learning-based algorithm for solving high-dimensional nonlinear backward stochastic differential equations (BSDEs), where the deep neural network (DNN) models are trained not only on the inputs and labels but also the differentials of the corresponding labels. This is motivated by the fact that differential deep learning can provide an efficient approximation of the labels and their derivatives with respect to inputs. The BSDEs are reformulated as differential deep learning problems by using Malliavin calculus. The Malliavin derivatives of solution to a BSDE satisfy themselves another BSDE, resulting thus in a system of BSDEs. Such formulation requires the estimation of the solution, its gradient, and the Hessian matrix, represented by the triple of processes $left(Y, Z, Gammaright).$ All the integrals within this system are discretized by using the Euler-Maruyama method. Subsequently, DNNs are employed to approximate the triple of these unknown processes. The DNN parameters are backwardly optimized at each time step by minimizing a differential learning type loss function, which is defined as a weighted sum of the dynamics of the discretized BSDE system, with the first term providing the dynamics of the process $Y$ and the other the process $Z$. An error analysis is carried out to show the convergence of the proposed algorithm. Various numerical experiments up to $50$ dimensions are provided to demonstrate the high efficiency. Both theoretically and numerically, it is demonstrated that our proposed scheme is more efficient compared to other contemporary deep learning-based methodologies, especially in the computation of the process $Gamma$.
{"title":"A backward differential deep learning-based algorithm for solving high-dimensional nonlinear backward stochastic differential equations","authors":"Lorenc Kapllani, Long Teng","doi":"arxiv-2404.08456","DOIUrl":"https://doi.org/arxiv-2404.08456","url":null,"abstract":"In this work, we propose a novel backward differential deep learning-based\u0000algorithm for solving high-dimensional nonlinear backward stochastic\u0000differential equations (BSDEs), where the deep neural network (DNN) models are\u0000trained not only on the inputs and labels but also the differentials of the\u0000corresponding labels. This is motivated by the fact that differential deep\u0000learning can provide an efficient approximation of the labels and their\u0000derivatives with respect to inputs. The BSDEs are reformulated as differential\u0000deep learning problems by using Malliavin calculus. The Malliavin derivatives\u0000of solution to a BSDE satisfy themselves another BSDE, resulting thus in a\u0000system of BSDEs. Such formulation requires the estimation of the solution, its\u0000gradient, and the Hessian matrix, represented by the triple of processes\u0000$left(Y, Z, Gammaright).$ All the integrals within this system are\u0000discretized by using the Euler-Maruyama method. Subsequently, DNNs are employed\u0000to approximate the triple of these unknown processes. The DNN parameters are\u0000backwardly optimized at each time step by minimizing a differential learning\u0000type loss function, which is defined as a weighted sum of the dynamics of the\u0000discretized BSDE system, with the first term providing the dynamics of the\u0000process $Y$ and the other the process $Z$. An error analysis is carried out to\u0000show the convergence of the proposed algorithm. Various numerical experiments\u0000up to $50$ dimensions are provided to demonstrate the high efficiency. Both\u0000theoretically and numerically, it is demonstrated that our proposed scheme is\u0000more efficient compared to other contemporary deep learning-based\u0000methodologies, especially in the computation of the process $Gamma$.","PeriodicalId":501294,"journal":{"name":"arXiv - QuantFin - Computational Finance","volume":"6 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140565999","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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