Pricing under rough volatility
Top Cited Papers
- 18 November 2015
- journal article
- research article
- Published by Taylor & Francis Ltd in Quantitative Finance
- Vol. 16 (6), 887-904
- https://doi.org/10.1080/14697688.2015.1099717
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.Keywords
Funding Information
- Deutsche Forschungsgemeinschaft (BA 5484/1-1)
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