We study an extension of the Heston stochastic volatility model that incorporates rough volatility and jump clustering phenomena. In our model, named the rough Hawkes Heston stochastic volatility model, the spot variance is a rough Hawkes-type process proportional to the intensity process of the...

We empirically investigate the functional link between the variance swap rate and the spot variance. Using S&P500 data over the period 2006-2018, we find overwhelming empirical evidence supporting the affine link analytically found by Kallsen et al. (2011) in the context of exponentially affine...

We propose a novel stochastic volatility model with price and volatility co-jumps driven by Hawkes processes and develop a feasible maximum-likelihood based procedure to estimate the parameters driving the jump intensity. Using S&P500 high-frequency prices over the period May 2007 - August 2021,...

In this paper we propose the first calibration exercise based on quantization methods. Pricing and calibration are typically difficult tasks to accomplish: pricing should be fast and accurate, otherwise calibration cannot be performed efficiently. We apply in a local volatility context the...

We develop a product functional quantization of rough volatility. Since the quantizers can be computed offline, this new technique, built on the insightful works by Luschgy and Pages, becomes a strong competitor in the new arena of numerical tools for rough volatility. We concentrate our...

In this paper we apply a new methodology based on quantization to price options in stochastic volatility models. This method can be applied to any model for which an Euler scheme is available for the underlying process and it allows for pricing vanillas, as well as exotics, thanks to the...