 Pricing under rough volatilityChristian Bayer, Peter Friz and Jim Gatheral Quantitative Finance, 2016, vol. 16, issue 6, 887-904 Abstract: From an analysis of the time series of realized variance using recent high-frequency data, Gatheral et al. [Volatility is rough, 2014] previously showed that the logarithm of realized variance behaves essentially as a fractional Brownian motion with Hurst exponent H of order 0.1, at any reasonable timescale. The resulting Rough Fractional Stochastic Volatility (RFSV) model is remarkably consistent with financial time series data. We now show how the RFSV model can be used to price claims on both the underlying and integrated variance. We analyse in detail a simple case of this model, the rBergomi model. In particular, we find that the rBergomi model fits the SPX volatility markedly better than conventional Markovian stochastic volatility models, and with fewer parameters. Finally, we show that actual SPX variance swap curves seem to be consistent with model forecasts, with particular dramatic examples from the weekend of the collapse of Lehman Brothers and the Flash Crash. Date: 2016 Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:taf:quantf:v:16:y:2016:i:6:p:887-904 Ordering information: This journal article can be ordered from DOI: 10.1080/14697688.2015.1099717 Access Statistics for this article Quantitative Finance is currently edited by Michael Dempster and Jim Gatheral More articles in Quantitative Finance from Taylor & Francis Journals |
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