# The characteristic function of rough Heston models

@article{ElEuch2016TheCF, title={The characteristic function of rough Heston models}, author={Omar El Euch and Mathieu Rosenbaum}, journal={Mathematical Finance}, year={2016}, volume={29}, pages={3 - 38} }

It has been recently shown that rough volatility models, where the volatility is driven by a fractional Brownian motion with small Hurst parameter, provide very relevant dynamics in order to reproduce the behavior of both historical and implied volatilities. However, due to the non‐Markovian nature of the fractional Brownian motion, they raise new issues when it comes to derivatives pricing. Using an original link between nearly unstable Hawkes processes and fractional volatility models, we…

## 198 Citations

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Rough volatility models are known to reproduce the behavior of historical volatility data while at the same time fitting the volatility surface remarkably well, with very few parameters. However,…

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This work provides a characterisation of the shortand long-maturity asymptotics of the implied volatility smile and reveals that the short-memory property precisely provides a jump-type behaviour of the smile for short maturities, thereby fixing the well-known standard inability of classical stochastic volatility models to fit theshort-end of the volatility smile.

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