{"title":"Stochastic Volatility of Volatility and Variance Risk Premia","authors":"O. Barndorff-Nielsen, Almut E. D. Veraart","doi":"10.2139/ssrn.1973121","DOIUrl":"https://doi.org/10.2139/ssrn.1973121","url":null,"abstract":"This article introduces a new class of stochastic volatility models which allows for stochastic volatility of volatility (SVV): Volatility modulated non-Gaussian Ornstein--Uhlenbeck (VMOU) processes. Various probabilistic properties of (integrated) VMOU processes are presented. Further we study the effect of the SVV on the leverage effect and on the presence of long memory. One of the key results in the article is that we can quantify the impact of the SVV on the (stochastic) dynamics of the variance risk premium (VRP). Moreover, provided the physical and the risk-neutral probability measures are related through a structure-preserving change of measure, we obtain an explicit formula for the VRP. Copyright The Author, 2012. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org , Oxford University Press.","PeriodicalId":187082,"journal":{"name":"ERN: Financial Market Volatility (Topic)","volume":"43 5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2011-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129484089","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The Smile in Stochastic Volatility Models","authors":"L. Bergomi, Julien Guyon","doi":"10.2139/ssrn.1967470","DOIUrl":"https://doi.org/10.2139/ssrn.1967470","url":null,"abstract":"We consider general stochastic volatility models with no local volatility component and derive the general expression of the volatility smile at order two in volatility-of-volatility. We show how, at this order, the smile only depends on three dimensionless numbers whose precise expressions as functionals of the model's spot/variance and variance/variance covariance functions we provide.Finally we assess the accuracy of our order two expansion using realistic levels of volatility-of-volatility.","PeriodicalId":187082,"journal":{"name":"ERN: Financial Market Volatility (Topic)","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2011-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116568860","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
M. Brière, J. Fermanian, Hassan Malongo, O. Signori
{"title":"Volatility Strategies for Global and Country Specific European Investors","authors":"M. Brière, J. Fermanian, Hassan Malongo, O. Signori","doi":"10.2139/ssrn.1945703","DOIUrl":"https://doi.org/10.2139/ssrn.1945703","url":null,"abstract":"Adding volatility exposure to an equity portfolio offers interesting opportunities for long-term investors. This article discusses the advantages of adding a long volatility strategy for a protection to a global European equity portfolio and to specific equity portfolios based in \"core\" or \"peripheral\" countries within the euro zone. A European investor today has the choice of investing in US or European equity volatility. We check whether a long volatility strategy based on VSTOXX futures is better than a strategy based on VIX futures. The benefit of using volatility strategies as a hedge for equities is shown through a Mean/Modified-CVaR portfolio optimization. We find that long volatility strategies offer valuable protection to all European equity investors. A long volatility strategy based on VSTOXX futures offers better protection than a similar one based on VIX futures. It reduces the risk of an equity portfolio more significantly, while providing more attractive returns. For specific European investors, and despite major differences in local European equity markets, our long volatility strategy shows a certain homogeneity and provides efficient protection, whatever the country.","PeriodicalId":187082,"journal":{"name":"ERN: Financial Market Volatility (Topic)","volume":"84 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2011-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124978169","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The Role of Volatility Shocks and Rare Events in Long-Run Risk Models","authors":"Nicole Branger, Paulo Rodrigues, Christian Schlag","doi":"10.2139/ssrn.2021070","DOIUrl":"https://doi.org/10.2139/ssrn.2021070","url":null,"abstract":"We generalize and extend the long-run risk model by Drechsler and Yaron (201'7 by separating the processes for the jump intensity and the stochastic conditional variance. Furthermore we replace their Ornstein-Uhlenbeck specification for the long-run mean of the conditional variance by a square-root process. Although these two modifications seem mainly technical at first sight they have major economic implications and change fundamental characteristics of the model. First they substantially improve the performance of the model in predictive regressions of future excess returns on the current price-dividend ratio and lead to an equity risk premium which is increasing not only with short-run but also with long-run uncertainty. Second, the decoupling of jump intensity and conditional variance permits a detailed analysis which of the effects first shown by Drechsler and Yaron (201'7 are due to the role of the conditional variance as a diffusive factor and which are caused by its second job, namely to control the likelihood of jumps. We find that for most effects generated by the model time-variation in the jump intensity is much more important than diffusive volatility risk.","PeriodicalId":187082,"journal":{"name":"ERN: Financial Market Volatility (Topic)","volume":"79 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2011-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130956247","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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