{"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}
引用次数: 1
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).
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