赫斯顿随机波动模型的降序建模

IF 0.7 4区数学 Q2 MATHEMATICS Hacettepe Journal of Mathematics and Statistics Pub Date : 2024-01-10 DOI:10.15672/hujms.1066143

Sinem Kozpinar, M. Uzunca, B. Karasözen

{"title":"赫斯顿随机波动模型的降序建模","authors":"Sinem Kozpinar, M. Uzunca, B. Karasözen","doi":"10.15672/hujms.1066143","DOIUrl":null,"url":null,"abstract":"In this paper, we compare the intrusive proper orthogonal decomposition (POD) with Galerkin projection and the data-driven dynamic mode decomposition (DMD), for Heston's option pricing model. The full order model is obtained by discontinuous Galerkin discretization in space and backward Euler in time. Numerical results for butterfly spread, European and digital call options reveal that in general DMD requires more modes than the POD modes for the same level of accuracy. However, the speed-up factors are much higher for DMD than POD due to the non-intrusive nature of the DMD.","PeriodicalId":55078,"journal":{"name":"Hacettepe Journal of Mathematics and Statistics","volume":"10 1","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2024-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Reduced-Order Modeling for Heston Stochastic Volatility Model\",\"authors\":\"Sinem Kozpinar, M. Uzunca, B. Karasözen\",\"doi\":\"10.15672/hujms.1066143\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we compare the intrusive proper orthogonal decomposition (POD) with Galerkin projection and the data-driven dynamic mode decomposition (DMD), for Heston's option pricing model. The full order model is obtained by discontinuous Galerkin discretization in space and backward Euler in time. Numerical results for butterfly spread, European and digital call options reveal that in general DMD requires more modes than the POD modes for the same level of accuracy. However, the speed-up factors are much higher for DMD than POD due to the non-intrusive nature of the DMD.\",\"PeriodicalId\":55078,\"journal\":{\"name\":\"Hacettepe Journal of Mathematics and Statistics\",\"volume\":\"10 1\",\"pages\":\"\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2024-01-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Hacettepe Journal of Mathematics and Statistics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.15672/hujms.1066143\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Hacettepe Journal of Mathematics and Statistics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.15672/hujms.1066143","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

本文比较了针对赫斯顿期权定价模型的侵入式适当正交分解（POD）、Galerkin 投影和数据驱动的动态模式分解（DMD）。全阶模型是通过空间的非连续 Galerkin 离散化和时间的反向欧拉离散化获得的。蝶式价差、欧式和数字看涨期权的数值结果表明，一般来说，在相同精度水平下，DMD 比 POD 模式需要更多的模式。然而，由于 DMD 的非侵入性，DMD 的加速因子要比 POD 高得多。

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

微信好友朋友圈 QQ好友复制链接

本刊更多论文

Reduced-Order Modeling for Heston Stochastic Volatility Model

In this paper, we compare the intrusive proper orthogonal decomposition (POD) with Galerkin projection and the data-driven dynamic mode decomposition (DMD), for Heston's option pricing model. The full order model is obtained by discontinuous Galerkin discretization in space and backward Euler in time. Numerical results for butterfly spread, European and digital call options reveal that in general DMD requires more modes than the POD modes for the same level of accuracy. However, the speed-up factors are much higher for DMD than POD due to the non-intrusive nature of the DMD.

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

Hacettepe Journal of Mathematics and Statistics 数学-数学

CiteScore

1.70

自引率

0.00%

发文量

100

审稿时长

6-12 weeks

期刊介绍： Hacettepe Journal of Mathematics and Statistics covers all aspects of Mathematics and Statistics. Papers on the interface between Mathematics and Statistics are particularly welcome, including applications to Physics, Actuarial Sciences, Finance and Economics. We strongly encourage submissions for Statistics Section including current and important real world examples across a wide range of disciplines. Papers have innovations of statistical methodology are highly welcome. Purely theoretical papers may be considered only if they include popular real world applications.