独立）从属关系与股票衍生品相关吗？

IF 1.3 4区数学 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Applied Stochastic Models in Business and Industry Pub Date : 2024-11-18 DOI:10.1002/asmb.2904

Michele Azzone, Roberto Baviera

{"title":"独立）从属关系与股票衍生品相关吗？","authors":"Michele Azzone, Roberto Baviera","doi":"10.1002/asmb.2904","DOIUrl":null,"url":null,"abstract":"Monroe (1978) demonstrates that any local semimartingale can be represented as a time‐changed Brownian Motion (BM). A natural question arises: does this representation theorem hold when the BM and the time‐change are independent? We prove that a local semimartingale is not equivalent to a BM with a time‐change that is independent from the BM. Our result is obtained utilizing a class of additive processes: the additive normal tempered stable (ATS). This class of processes exhibits an exceptional ability to calibrate the equity volatility surface accurately. We notice that the sub‐class of additive processes that can be obtained with an independent additive subordination is incompatible with market data and shows significantly worse calibration performances than the ATS, especially on short time maturities. These results have been observed every business day in a semester on a dataset of S&P 500 and EURO STOXX 50 options.","PeriodicalId":55495,"journal":{"name":"Applied Stochastic Models in Business and Industry","volume":"22 1","pages":""},"PeriodicalIF":1.3000,"publicationDate":"2024-11-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Is (Independent) Subordination Relevant in Equity Derivatives?\",\"authors\":\"Michele Azzone, Roberto Baviera\",\"doi\":\"10.1002/asmb.2904\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Monroe (1978) demonstrates that any local semimartingale can be represented as a time‐changed Brownian Motion (BM). A natural question arises: does this representation theorem hold when the BM and the time‐change are independent? We prove that a local semimartingale is not equivalent to a BM with a time‐change that is independent from the BM. Our result is obtained utilizing a class of additive processes: the additive normal tempered stable (ATS). This class of processes exhibits an exceptional ability to calibrate the equity volatility surface accurately. We notice that the sub‐class of additive processes that can be obtained with an independent additive subordination is incompatible with market data and shows significantly worse calibration performances than the ATS, especially on short time maturities. These results have been observed every business day in a semester on a dataset of S&P 500 and EURO STOXX 50 options.\",\"PeriodicalId\":55495,\"journal\":{\"name\":\"Applied Stochastic Models in Business and Industry\",\"volume\":\"22 1\",\"pages\":\"\"},\"PeriodicalIF\":1.3000,\"publicationDate\":\"2024-11-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Applied Stochastic Models in Business and Industry\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1002/asmb.2904\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Stochastic Models in Business and Industry","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1002/asmb.2904","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}

引用次数: 0

摘要

门罗（Monroe）（1978 年）证明，任何局部半马尔廷格都可以表示为时变布朗运动（BM）。一个自然的问题随之而来：当 BM 和时间变化相互独立时，这一表示定理是否成立？我们证明，局部半鞅并不等同于时变独立于 BM 的 BM。我们的结果是利用一类加法过程得出的：加法正态节制稳定（ATS）。这一类过程在精确校准股票波动率表面方面表现出非凡的能力。我们注意到，用独立的加法隶属度得到的加法过程子类与市场数据不符，其校准性能明显不如 ATS，尤其是在短时间期限上。在 S&P 500 和 EURO STOXX 50 期权数据集上，我们在一个学期的每个工作日都观察到了这些结果。

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

Is (Independent) Subordination Relevant in Equity Derivatives?

Monroe (1978) demonstrates that any local semimartingale can be represented as a time‐changed Brownian Motion (BM). A natural question arises: does this representation theorem hold when the BM and the time‐change are independent? We prove that a local semimartingale is not equivalent to a BM with a time‐change that is independent from the BM. Our result is obtained utilizing a class of additive processes: the additive normal tempered stable (ATS). This class of processes exhibits an exceptional ability to calibrate the equity volatility surface accurately. We notice that the sub‐class of additive processes that can be obtained with an independent additive subordination is incompatible with market data and shows significantly worse calibration performances than the ATS, especially on short time maturities. These results have been observed every business day in a semester on a dataset of S&P 500 and EURO STOXX 50 options.

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

Applied Stochastic Models in Business and Industry 数学-数学跨学科应用

CiteScore

2.70

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： ASMBI - Applied Stochastic Models in Business and Industry (formerly Applied Stochastic Models and Data Analysis) was first published in 1985, publishing contributions in the interface between stochastic modelling, data analysis and their applications in business, finance, insurance, management and production. In 2007 ASMBI became the official journal of the International Society for Business and Industrial Statistics (www.isbis.org). The main objective is to publish papers, both technical and practical, presenting new results which solve real-life problems or have great potential in doing so. Mathematical rigour, innovative stochastic modelling and sound applications are the key ingredients of papers to be published, after a very selective review process. The journal is very open to new ideas, like Data Science and Big Data stemming from problems in business and industry or uncertainty quantification in engineering, as well as more traditional ones, like reliability, quality control, design of experiments, managerial processes, supply chains and inventories, insurance, econometrics, financial modelling (provided the papers are related to real problems). The journal is interested also in papers addressing the effects of business and industrial decisions on the environment, healthcare, social life. State-of-the art computational methods are very welcome as well, when combined with sound applications and innovative models.