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 …

We introduce affine Volterra processes, defined as solutions of certain stochastic
convolution equations with affine coefficients. Classical affine diffusions constitute a special …

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 …

We show that typical behaviors of market participants at the high frequency scale generate
leverage effect and rough volatility. To do so, we build a simple microscopic model for the …

It has been recently shown that spot volatilities can be closely modeled by rough stochastic
volatility-type dynamics. In such models, the log-volatility follows a fractional Brownian …

The Black–Scholes implied volatility skew at the money of SPX options is known to obey a
power law with respect to the time to maturity. We construct a model of the underlying asset …

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 …

Malliavin Calculus in Finance: Theory and Practice aims to introduce the study of stochastic
volatility (SV) models via Malliavin Calculus. Malliavin calculus has had a profound impact …

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We discuss the pricing and hedging of volatility options in some rough volatility models. First,
we develop efficient Monte Carlo methods and asymptotic approximations for computing …