SABR随机波动模型的人工神经网络表示

IF 0.8 4区经济学 Q4 BUSINESS, FINANCE

Journal of Computational Finance Pub Date : 2021-01-01 DOI:10.21314/jcf.2021.007

William McGhee

{"title":"SABR随机波动模型的人工神经网络表示","authors":"William McGhee","doi":"10.21314/jcf.2021.007","DOIUrl":null,"url":null,"abstract":"In this article, the Universal Approximation Theorem of Artificial Neural Networks (ANNs) is applied to the SABR stochastic volatility model in order to construct highly efficient representations. Initially, the SABR approximation of Hagan et al. [2002] is considered, then a more accurate integration scheme of McGhee [2011] as well as a two factor finite difference scheme. The resulting ANN calculates 10,000 times faster than the finite difference scheme whilst maintaining a high degree of accuracy. As a result, the ANN dispenses with the need for the commonly used SABR Approximation.","PeriodicalId":51731,"journal":{"name":"Journal of Computational Finance","volume":"5 1","pages":""},"PeriodicalIF":0.8000,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"An artificial neural network representation of the SABR stochastic volatility model\",\"authors\":\"William McGhee\",\"doi\":\"10.21314/jcf.2021.007\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this article, the Universal Approximation Theorem of Artificial Neural Networks (ANNs) is applied to the SABR stochastic volatility model in order to construct highly efficient representations. Initially, the SABR approximation of Hagan et al. [2002] is considered, then a more accurate integration scheme of McGhee [2011] as well as a two factor finite difference scheme. The resulting ANN calculates 10,000 times faster than the finite difference scheme whilst maintaining a high degree of accuracy. As a result, the ANN dispenses with the need for the commonly used SABR Approximation.\",\"PeriodicalId\":51731,\"journal\":{\"name\":\"Journal of Computational Finance\",\"volume\":\"5 1\",\"pages\":\"\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2021-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Computational Finance\",\"FirstCategoryId\":\"96\",\"ListUrlMain\":\"https://doi.org/10.21314/jcf.2021.007\",\"RegionNum\":4,\"RegionCategory\":\"经济学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"BUSINESS, FINANCE\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Computational Finance","FirstCategoryId":"96","ListUrlMain":"https://doi.org/10.21314/jcf.2021.007","RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"BUSINESS, FINANCE","Score":null,"Total":0}

引用次数: 0

摘要

本文将人工神经网络的通用逼近定理应用于SABR随机波动模型，以构造高效的表示。首先考虑Hagan等[2002]的SABR近似，然后考虑McGhee[2011]的更精确的积分格式以及两因子有限差分格式。由此产生的人工神经网络的计算速度比有限差分方案快10,000倍，同时保持了高度的准确性。因此，人工神经网络省去了常用的SABR近似的需要。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

An artificial neural network representation of the SABR stochastic volatility model

In this article, the Universal Approximation Theorem of Artificial Neural Networks (ANNs) is applied to the SABR stochastic volatility model in order to construct highly efficient representations. Initially, the SABR approximation of Hagan et al. [2002] is considered, then a more accurate integration scheme of McGhee [2011] as well as a two factor finite difference scheme. The resulting ANN calculates 10,000 times faster than the finite difference scheme whilst maintaining a high degree of accuracy. As a result, the ANN dispenses with the need for the commonly used SABR Approximation.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Journal of Computational Finance BUSINESS, FINANCE-

CiteScore

0.90

自引率

0.00%

发文量

期刊介绍： The Journal of Computational Finance is an international peer-reviewed journal dedicated to advancing knowledge in the area of financial mathematics. The journal is focused on the measurement, management and analysis of financial risk, and provides detailed insight into numerical and computational techniques in the pricing, hedging and risk management of financial instruments. The journal welcomes papers dealing with innovative computational techniques in the following areas: Numerical solutions of pricing equations: finite differences, finite elements, and spectral techniques in one and multiple dimensions. Simulation approaches in pricing and risk management: advances in Monte Carlo and quasi-Monte Carlo methodologies; new strategies for market factors simulation. Optimization techniques in hedging and risk management. Fundamental numerical analysis relevant to finance: effect of boundary treatments on accuracy; new discretization of time-series analysis. Developments in free-boundary problems in finance: alternative ways and numerical implications in American option pricing.