{"title":"OPTION IMPLIED VIX, SKEW AND KURTOSIS TERM STRUCTURES","authors":"DILIP B. MADAN, KING WANG","doi":"10.1142/s0219024921500308","DOIUrl":null,"url":null,"abstract":"Comparisons are made of the Chicago Board of Options Exchange (CBOE) skew index with those derived from parametric skews of bilateral gamma models and from the differentiation of option implied characteristic exponents. Discrepancies can be due to strike discretization in evaluating prices of powered returns. The remedy suggested employs a finer and wider set of strikes obtaining additional option prices by interpolation and extrapolation of implied volatilities. Procedures of replicating powered return claims are applied to the fourth power and the derivation of kurtosis term structures. Regressions of log skewness and log excess kurtosis on log maturity confirm the positivity of decay in these higher moments. The decay rates are below those required by processes of independent and identically distributed increments.","PeriodicalId":47022,"journal":{"name":"International Journal of Theoretical and Applied Finance","volume":null,"pages":null},"PeriodicalIF":0.5000,"publicationDate":"2021-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Theoretical and Applied Finance","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1142/s0219024921500308","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"BUSINESS, FINANCE","Score":null,"Total":0}
引用次数: 0
Abstract
Comparisons are made of the Chicago Board of Options Exchange (CBOE) skew index with those derived from parametric skews of bilateral gamma models and from the differentiation of option implied characteristic exponents. Discrepancies can be due to strike discretization in evaluating prices of powered returns. The remedy suggested employs a finer and wider set of strikes obtaining additional option prices by interpolation and extrapolation of implied volatilities. Procedures of replicating powered return claims are applied to the fourth power and the derivation of kurtosis term structures. Regressions of log skewness and log excess kurtosis on log maturity confirm the positivity of decay in these higher moments. The decay rates are below those required by processes of independent and identically distributed increments.
期刊介绍：
The shift of the financial market towards the general use of advanced mathematical methods has led to the introduction of state-of-the-art quantitative tools into the world of finance. The International Journal of Theoretical and Applied Finance (IJTAF) brings together international experts involved in the mathematical modelling of financial instruments as well as the application of these models to global financial markets. The development of complex financial products has led to new challenges to the regulatory bodies. Financial instruments that have been designed to serve the needs of the mature capitals market need to be adapted for application in the emerging markets.
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