{"title":"百慕大期权的模拟最优行使边界","authors":"Dejun Xie, David A. Edwards, Xiaoxia Wu","doi":"10.1142/s242478632250013x","DOIUrl":null,"url":null,"abstract":"In this paper, a novel algorithm for determining the free exercise boundary for high-dimensional Bermudan option problems is presented. First, a rough estimate of the boundary is constructed on a fine (daily) time grid. This rough estimate is used to generate a more accurate estimate on a coarse time grid (exercise opportunities). Antithetic branching is used to reduce the computational workload. The method is validated by comparing it with other methods of solving the standard Black–Scholes problem. Finally, the method is applied to two cases of Bermudan options with a second stochastic variable: a stochastic interest rate and a stochastic volatility.","PeriodicalId":54088,"journal":{"name":"International Journal of Financial Engineering","volume":" ","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2022-04-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Optimal exercise frontier of Bermudan options by simulation methods\",\"authors\":\"Dejun Xie, David A. Edwards, Xiaoxia Wu\",\"doi\":\"10.1142/s242478632250013x\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, a novel algorithm for determining the free exercise boundary for high-dimensional Bermudan option problems is presented. First, a rough estimate of the boundary is constructed on a fine (daily) time grid. This rough estimate is used to generate a more accurate estimate on a coarse time grid (exercise opportunities). Antithetic branching is used to reduce the computational workload. The method is validated by comparing it with other methods of solving the standard Black–Scholes problem. Finally, the method is applied to two cases of Bermudan options with a second stochastic variable: a stochastic interest rate and a stochastic volatility.\",\"PeriodicalId\":54088,\"journal\":{\"name\":\"International Journal of Financial Engineering\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2022-04-14\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Journal of Financial Engineering\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1142/s242478632250013x\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"BUSINESS, FINANCE\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Financial Engineering","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1142/s242478632250013x","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"BUSINESS, FINANCE","Score":null,"Total":0}
Optimal exercise frontier of Bermudan options by simulation methods
In this paper, a novel algorithm for determining the free exercise boundary for high-dimensional Bermudan option problems is presented. First, a rough estimate of the boundary is constructed on a fine (daily) time grid. This rough estimate is used to generate a more accurate estimate on a coarse time grid (exercise opportunities). Antithetic branching is used to reduce the computational workload. The method is validated by comparing it with other methods of solving the standard Black–Scholes problem. Finally, the method is applied to two cases of Bermudan options with a second stochastic variable: a stochastic interest rate and a stochastic volatility.
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