A new paradigm has emerged recently in financial modeling: rough (stochastic) volatility.
First observed by Gatheral et al. in high‐frequency data, subsequently derived within market …

Since we will never really know why the prices of financial assets move, we should at least
make a faithful model of how they move. This was the motivation of Bachelier in 1900, when …

We consider rough stochastic volatility models where the driving noise of volatility has
fractional scaling, in the 'rough'regime of Hurst parameter H< 1/2. This regime recently …

Asymptotic analysis of stochastic stock price models is the central topic of the present
volume. Special examples of such models are stochastic volatility models, that have been …

We introduce and compare computational techniques for sharp extreme event probability
estimates in stochastic differential equations with small additive Gaussian noise. In …

We present a new methodology to analyze large classes of (classical and rough) stochastic
volatility models, with special regard to short-time and small noise formulae for option prices …

Sharp large deviation estimates for stochastic differential equations with small noise, based
on minimizing the Freidlin–Wentzell action functional under appropriate boundary …

Introduced recently in mathematical finance by Bayer et al.(2016), the rough Bergomi model
has proved particularly efficient to calibrate option markets. We investigate some of its …

Abstract Avellaneda et al.(2002, 2003) pioneered the pricing and hedging of index options–
products highly sensitive to implied volatility and correlation assumptions–with large …

In Part I (Comm. Pure Appl. Math., 67 (2014), no. 1, 40–82) we discussed density
expansions for multidimensional diffusions (X1,…, Xd), at fixed time T and projected to their …