{"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}
引用次数: 0
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.
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.
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