Rough volatility models are known to fit the volatility surface remarkably well with very few parameters. On the other hand, the classical Heston model is highly tractable allowing for fast calibration. We present here the rough Heston model which offers the best of both worlds. Even better, we...

A small-time Edgeworth expansion of the density of an asset price is given under a general stochastic volatility model, from which asymptotic expansions of put option prices and at-the-money implied volatilities follow. A limit theorem for at-the-money implied volatility skew and curvature is...

Previous literature has identified an effect, dubbed the Zumbach effect, that is nonzero empirically but conjectured to be zero in any conventional stochastic volatility model. Essentially this effect corresponds to the property that past squared returns forecast future volatilities better than...

From an analysis of the time series of volatility using recent high frequency data, Gatheral, Jaisson and Rosenbaum previously showed that log-volatility behaves essentially as a fractional Brownian motion with Hurst exponent H of order 0.1, at any reasonable time scale. The resulting Rough...

Assuming local volatility, we derive an exact Brownian bridge representation for the transition density; an exact expression for the transition density in terms of a path integral then follows. By Taylor-expanding around a certain path, we obtain a generalization of the heat kernel expansion of...

In this article, we show how to calibrate the widely-used SVI parameterization of the implied volatility smile in such a way as to guarantee the absence of static arbitrage. In particular, we exhibit a large class of arbitrage-free SVI volatility surfaces with a simple closed-form...