{"title":"正态和正态逼近在期权和股票组合风险度量中的应用","authors":"E. Sulistianingsih., D. Rosadi, Abdurakhman","doi":"10.1063/1.5139181","DOIUrl":null,"url":null,"abstract":"Measuring risk of a portfolio comprising of multi assets such as option and stock by Value at Risk (VaR) will become more challenging because unlike stock price, value of an option has a nonlinear dependence on market risk factor. This paper considered to utilize Delta Normal and Delta Gamma Normal as a linear approach of the factor determining price of the assets. The methods use consecutively the expansion of first and second-order Taylor Series to approximate the profit loss, which is prominent to develop VaR of a multi-asset portfolio. As an application of these methods, this paper analyzed a portfolio comprising of one stock (Exxon Mobile Corporation (XOM)) and two options from two different enterprises, namely JD.com, Inc. (JD), and Eni. S.p. A (E). According to Kupiec Backtesting, it can be concluded that in this case, VaR Delta Normal and VaR Delta Gamma Normal Models provide a good risk measurement at some different confidence levels (90, 95, and 99 percent).Measuring risk of a portfolio comprising of multi assets such as option and stock by Value at Risk (VaR) will become more challenging because unlike stock price, value of an option has a nonlinear dependence on market risk factor. This paper considered to utilize Delta Normal and Delta Gamma Normal as a linear approach of the factor determining price of the assets. The methods use consecutively the expansion of first and second-order Taylor Series to approximate the profit loss, which is prominent to develop VaR of a multi-asset portfolio. As an application of these methods, this paper analyzed a portfolio comprising of one stock (Exxon Mobile Corporation (XOM)) and two options from two different enterprises, namely JD.com, Inc. (JD), and Eni. S.p. A (E). According to Kupiec Backtesting, it can be concluded that in this case, VaR Delta Normal and VaR Delta Gamma Normal Models provide a good risk measurement at some different confidence levels (90, 95, and 99 percent).","PeriodicalId":209108,"journal":{"name":"PROCEEDINGS OF THE 8TH SEAMS-UGM INTERNATIONAL CONFERENCE ON MATHEMATICS AND ITS APPLICATIONS 2019: Deepening Mathematical Concepts for Wider Application through Multidisciplinary Research and Industries Collaborations","volume":"11 2","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2019-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Delta normal and delta gamma normal approximation in risk measurement of portfolio consisted of option and stock\",\"authors\":\"E. Sulistianingsih., D. Rosadi, Abdurakhman\",\"doi\":\"10.1063/1.5139181\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Measuring risk of a portfolio comprising of multi assets such as option and stock by Value at Risk (VaR) will become more challenging because unlike stock price, value of an option has a nonlinear dependence on market risk factor. This paper considered to utilize Delta Normal and Delta Gamma Normal as a linear approach of the factor determining price of the assets. The methods use consecutively the expansion of first and second-order Taylor Series to approximate the profit loss, which is prominent to develop VaR of a multi-asset portfolio. As an application of these methods, this paper analyzed a portfolio comprising of one stock (Exxon Mobile Corporation (XOM)) and two options from two different enterprises, namely JD.com, Inc. (JD), and Eni. S.p. A (E). According to Kupiec Backtesting, it can be concluded that in this case, VaR Delta Normal and VaR Delta Gamma Normal Models provide a good risk measurement at some different confidence levels (90, 95, and 99 percent).Measuring risk of a portfolio comprising of multi assets such as option and stock by Value at Risk (VaR) will become more challenging because unlike stock price, value of an option has a nonlinear dependence on market risk factor. This paper considered to utilize Delta Normal and Delta Gamma Normal as a linear approach of the factor determining price of the assets. The methods use consecutively the expansion of first and second-order Taylor Series to approximate the profit loss, which is prominent to develop VaR of a multi-asset portfolio. As an application of these methods, this paper analyzed a portfolio comprising of one stock (Exxon Mobile Corporation (XOM)) and two options from two different enterprises, namely JD.com, Inc. (JD), and Eni. S.p. A (E). According to Kupiec Backtesting, it can be concluded that in this case, VaR Delta Normal and VaR Delta Gamma Normal Models provide a good risk measurement at some different confidence levels (90, 95, and 99 percent).\",\"PeriodicalId\":209108,\"journal\":{\"name\":\"PROCEEDINGS OF THE 8TH SEAMS-UGM INTERNATIONAL CONFERENCE ON MATHEMATICS AND ITS APPLICATIONS 2019: Deepening Mathematical Concepts for Wider Application through Multidisciplinary Research and Industries Collaborations\",\"volume\":\"11 2\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2019-12-19\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"PROCEEDINGS OF THE 8TH SEAMS-UGM INTERNATIONAL CONFERENCE ON MATHEMATICS AND ITS APPLICATIONS 2019: Deepening Mathematical Concepts for Wider Application through Multidisciplinary Research and Industries Collaborations\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1063/1.5139181\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"PROCEEDINGS OF THE 8TH SEAMS-UGM INTERNATIONAL CONFERENCE ON MATHEMATICS AND ITS APPLICATIONS 2019: Deepening Mathematical Concepts for Wider Application through Multidisciplinary Research and Industries Collaborations","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1063/1.5139181","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Delta normal and delta gamma normal approximation in risk measurement of portfolio consisted of option and stock
Measuring risk of a portfolio comprising of multi assets such as option and stock by Value at Risk (VaR) will become more challenging because unlike stock price, value of an option has a nonlinear dependence on market risk factor. This paper considered to utilize Delta Normal and Delta Gamma Normal as a linear approach of the factor determining price of the assets. The methods use consecutively the expansion of first and second-order Taylor Series to approximate the profit loss, which is prominent to develop VaR of a multi-asset portfolio. As an application of these methods, this paper analyzed a portfolio comprising of one stock (Exxon Mobile Corporation (XOM)) and two options from two different enterprises, namely JD.com, Inc. (JD), and Eni. S.p. A (E). According to Kupiec Backtesting, it can be concluded that in this case, VaR Delta Normal and VaR Delta Gamma Normal Models provide a good risk measurement at some different confidence levels (90, 95, and 99 percent).Measuring risk of a portfolio comprising of multi assets such as option and stock by Value at Risk (VaR) will become more challenging because unlike stock price, value of an option has a nonlinear dependence on market risk factor. This paper considered to utilize Delta Normal and Delta Gamma Normal as a linear approach of the factor determining price of the assets. The methods use consecutively the expansion of first and second-order Taylor Series to approximate the profit loss, which is prominent to develop VaR of a multi-asset portfolio. As an application of these methods, this paper analyzed a portfolio comprising of one stock (Exxon Mobile Corporation (XOM)) and two options from two different enterprises, namely JD.com, Inc. (JD), and Eni. S.p. A (E). According to Kupiec Backtesting, it can be concluded that in this case, VaR Delta Normal and VaR Delta Gamma Normal Models provide a good risk measurement at some different confidence levels (90, 95, and 99 percent).
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