{"title":"Deep Signature Algorithm for Multidimensional Path-Dependent Options","authors":"Erhan Bayraktar, Qi Feng, Zhaoyu Zhang","doi":"10.1137/23m1571563","DOIUrl":null,"url":null,"abstract":"SIAM Journal on Financial Mathematics, Volume 15, Issue 1, Page 194-214, March 2024. <br/> Abstract. In this work, we study the deep signature algorithms for path-dependent options. We extend the backward scheme in [C. Huré, H. Pham, and X. Warin, Math. Comp., 89 (2020), pp. 1547–1579] for state-dependent FBSDEs with reflections to path-dependent FBSDEs with reflections, by adding the signature layer to the backward scheme. Our algorithm applies to both European and American type option pricing problems, while the payoff function depends on the whole paths of the underlying forward stock process. We prove the convergence analysis of our numerical algorithm with explicit dependence on the truncation order of the signature and the neural network approximation errors. Numerical examples for the algorithm are provided, including Amerasian option under the Black–Scholes model, American option with a path-dependent geometric mean payoff function, and Shiryaev’s optimal stopping problem.","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2024-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"96","ListUrlMain":"https://doi.org/10.1137/23m1571563","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
SIAM Journal on Financial Mathematics, Volume 15, Issue 1, Page 194-214, March 2024. Abstract. In this work, we study the deep signature algorithms for path-dependent options. We extend the backward scheme in [C. Huré, H. Pham, and X. Warin, Math. Comp., 89 (2020), pp. 1547–1579] for state-dependent FBSDEs with reflections to path-dependent FBSDEs with reflections, by adding the signature layer to the backward scheme. Our algorithm applies to both European and American type option pricing problems, while the payoff function depends on the whole paths of the underlying forward stock process. We prove the convergence analysis of our numerical algorithm with explicit dependence on the truncation order of the signature and the neural network approximation errors. Numerical examples for the algorithm are provided, including Amerasian option under the Black–Scholes model, American option with a path-dependent geometric mean payoff function, and Shiryaev’s optimal stopping problem.
期刊介绍：
Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance.
Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.
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