{"title":"为欧洲和亚洲期权定价的新型高阶高效计算方法","authors":"Saurabh Bansal, Srinivasan Natesan","doi":"10.1007/s11075-024-01909-6","DOIUrl":null,"url":null,"abstract":"<p>In this article, we present a fourth-order accurate numerical method for solving generalized Black-Scholes PDE describing European and Asian options. Initially, we discretize the time derivative by the Crank-Nicolson scheme, and then the resultant semi-discrete problem by the central difference scheme on uniform meshes. In order to enhance the order of convergence of the proposed scheme, we employ the Richardson extrapolation method, by using two different meshes to solve the fully discrete problem. The stability and convergence are studied. To validate the proposed technique, several numerical experiments are carried out.</p>","PeriodicalId":54709,"journal":{"name":"Numerical Algorithms","volume":"2 1","pages":""},"PeriodicalIF":1.7000,"publicationDate":"2024-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A novel higher-order efficient computational method for pricing European and Asian options\",\"authors\":\"Saurabh Bansal, Srinivasan Natesan\",\"doi\":\"10.1007/s11075-024-01909-6\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>In this article, we present a fourth-order accurate numerical method for solving generalized Black-Scholes PDE describing European and Asian options. Initially, we discretize the time derivative by the Crank-Nicolson scheme, and then the resultant semi-discrete problem by the central difference scheme on uniform meshes. In order to enhance the order of convergence of the proposed scheme, we employ the Richardson extrapolation method, by using two different meshes to solve the fully discrete problem. The stability and convergence are studied. To validate the proposed technique, several numerical experiments are carried out.</p>\",\"PeriodicalId\":54709,\"journal\":{\"name\":\"Numerical Algorithms\",\"volume\":\"2 1\",\"pages\":\"\"},\"PeriodicalIF\":1.7000,\"publicationDate\":\"2024-08-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Numerical Algorithms\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s11075-024-01909-6\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Numerical Algorithms","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s11075-024-01909-6","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
A novel higher-order efficient computational method for pricing European and Asian options
In this article, we present a fourth-order accurate numerical method for solving generalized Black-Scholes PDE describing European and Asian options. Initially, we discretize the time derivative by the Crank-Nicolson scheme, and then the resultant semi-discrete problem by the central difference scheme on uniform meshes. In order to enhance the order of convergence of the proposed scheme, we employ the Richardson extrapolation method, by using two different meshes to solve the fully discrete problem. The stability and convergence are studied. To validate the proposed technique, several numerical experiments are carried out.
期刊介绍:
The journal Numerical Algorithms is devoted to numerical algorithms. It publishes original and review papers on all the aspects of numerical algorithms: new algorithms, theoretical results, implementation, numerical stability, complexity, parallel computing, subroutines, and applications. Papers on computer algebra related to obtaining numerical results will also be considered. It is intended to publish only high quality papers containing material not published elsewhere.