We consider the three factor double mean reverting (DMR) model of Gatheral (2008), a model which can be successfully calibrated to both VIX options and SPX options simultaneously. One drawback of this model is that calibration may be slow because no closed form solution for European options...

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...

In this short note, we prove by an appropriate change of variables that the SVI implied volatility parameterization presented in Gatheral's book and the large-time asymptotic of the Heston implied volatility agree algebraically, thus confirming a conjecture from Gatheral as well as providing a...

Optimal execution in financial markets is the problem of how to trade a large quantity of shares incrementally in time in order to minimise the expected cost. In this paper we study the problem of the optimal execution in the presence of nonlinear transient market impact. Mathematically such...

We study the problem of the optimal execution of a large trade in the propagator model with nonlinear transient impact. From brute force numerical optimization of the cost functional, we find that the optimal solution for a buy program typically features a few short intense buying periods...

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...