{"title":"更改数字","authors":"T. Björk","doi":"10.1002/9780470061602.EQF04010","DOIUrl":null,"url":null,"abstract":"In this chapter we discuss how a suitable change of numeraire and the corresponding change of martingale measure, can simplify the computation of pricing formula for financial derivatives. We derive a general formula for the likelihood process related to an arbitrary numeraire, and we identify the corresponding Girsanov transformation. As an example, we compute the price of an exchange option. In particular we study the class of forward measures related to zero coupon bonds and we derive a general option pricing formula. As an application of the general theory we also study the so-called numeraire portfolio.","PeriodicalId":311283,"journal":{"name":"Arbitrage Theory in Continuous Time","volume":"1 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2010-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Change of Numeraire\",\"authors\":\"T. Björk\",\"doi\":\"10.1002/9780470061602.EQF04010\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this chapter we discuss how a suitable change of numeraire and the corresponding change of martingale measure, can simplify the computation of pricing formula for financial derivatives. We derive a general formula for the likelihood process related to an arbitrary numeraire, and we identify the corresponding Girsanov transformation. As an example, we compute the price of an exchange option. In particular we study the class of forward measures related to zero coupon bonds and we derive a general option pricing formula. As an application of the general theory we also study the so-called numeraire portfolio.\",\"PeriodicalId\":311283,\"journal\":{\"name\":\"Arbitrage Theory in Continuous Time\",\"volume\":\"1 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2010-05-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Arbitrage Theory in Continuous Time\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1002/9780470061602.EQF04010\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Arbitrage Theory in Continuous Time","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1002/9780470061602.EQF04010","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
In this chapter we discuss how a suitable change of numeraire and the corresponding change of martingale measure, can simplify the computation of pricing formula for financial derivatives. We derive a general formula for the likelihood process related to an arbitrary numeraire, and we identify the corresponding Girsanov transformation. As an example, we compute the price of an exchange option. In particular we study the class of forward measures related to zero coupon bonds and we derive a general option pricing formula. As an application of the general theory we also study the so-called numeraire portfolio.
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