{"title":"无正态假设的Black-Scholes公式:在随机波动率和随机利率中的应用","authors":"Moawia Alghalith","doi":"10.2139/ssrn.3918488","DOIUrl":null,"url":null,"abstract":"We provide explicit, simple price formulas for the European options under stochastic volatility and stochastic interest rate. The formulas are as simple as the classical Black-Scholes formula. Moreover, the formulas do not require the normality of the returns. We do not need to know the distribution of the returns/price.","PeriodicalId":209192,"journal":{"name":"ERN: Asset Pricing Models (Topic)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2021-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Black-Scholes formulas without the normality assumption: Applications to stochastic volatility and stochastic interest rate\",\"authors\":\"Moawia Alghalith\",\"doi\":\"10.2139/ssrn.3918488\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We provide explicit, simple price formulas for the European options under stochastic volatility and stochastic interest rate. The formulas are as simple as the classical Black-Scholes formula. Moreover, the formulas do not require the normality of the returns. We do not need to know the distribution of the returns/price.\",\"PeriodicalId\":209192,\"journal\":{\"name\":\"ERN: Asset Pricing Models (Topic)\",\"volume\":\"1 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2021-09-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"ERN: Asset Pricing Models (Topic)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.2139/ssrn.3918488\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"ERN: Asset Pricing Models (Topic)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2139/ssrn.3918488","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Black-Scholes formulas without the normality assumption: Applications to stochastic volatility and stochastic interest rate
We provide explicit, simple price formulas for the European options under stochastic volatility and stochastic interest rate. The formulas are as simple as the classical Black-Scholes formula. Moreover, the formulas do not require the normality of the returns. We do not need to know the distribution of the returns/price.