{"title":"Option pricing in a stochastic delay volatility model","authors":"Álvaro Guinea Juliá, Raquel Caro-Carretero","doi":"10.1002/mma.10417","DOIUrl":null,"url":null,"abstract":"<p>This work introduces a new stochastic volatility model with delay parameters in the volatility process, extending the Barndorff–Nielsen and Shephard model. It establishes an analytical expression for the log price characteristic function, which can be applied to price European options. Empirical analysis on S&P500 European call options shows that adding delay parameters reduces mean squared error. This is the first instance of providing an analytical formula for the log price characteristic function in a stochastic volatility model with multiple delay parameters. We also provide a Monte Carlo scheme that can be used to simulate the model.</p>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 2","pages":"1927-1951"},"PeriodicalIF":1.8000,"publicationDate":"2024-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mma.10417","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Methods in the Applied Sciences","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/mma.10417","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
This work introduces a new stochastic volatility model with delay parameters in the volatility process, extending the Barndorff–Nielsen and Shephard model. It establishes an analytical expression for the log price characteristic function, which can be applied to price European options. Empirical analysis on S&P500 European call options shows that adding delay parameters reduces mean squared error. This is the first instance of providing an analytical formula for the log price characteristic function in a stochastic volatility model with multiple delay parameters. We also provide a Monte Carlo scheme that can be used to simulate the model.
期刊介绍：
Mathematical Methods in the Applied Sciences publishes papers dealing with new mathematical methods for the consideration of linear and non-linear, direct and inverse problems for physical relevant processes over time- and space- varying media under certain initial, boundary, transition conditions etc. Papers dealing with biomathematical content, population dynamics and network problems are most welcome.
Mathematical Methods in the Applied Sciences is an interdisciplinary journal: therefore, all manuscripts must be written to be accessible to a broad scientific but mathematically advanced audience. All papers must contain carefully written introduction and conclusion sections, which should include a clear exposition of the underlying scientific problem, a summary of the mathematical results and the tools used in deriving the results. Furthermore, the scientific importance of the manuscript and its conclusions should be made clear. Papers dealing with numerical processes or which contain only the application of well established methods will not be accepted.
Because of the broad scope of the journal, authors should minimize the use of technical jargon from their subfield in order to increase the accessibility of their paper and appeal to a wider readership. If technical terms are necessary, authors should define them clearly so that the main ideas are understandable also to readers not working in the same subfield.
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