Comparing Rough Volatility Models

Since the introduction of rough volatility there have been numerous attempts at combining it with existing models in order to better approximate the volatility surface with a low number of parameters. The drawback of rough volatility is usually the time needed to compute a volatility surface. We compare three major rough volatility models and...

Run-and-Tumble Motion: The Role of Reversibility

We study a model of active particles that perform a simple random walk and on top of that have a preferred direction determined by an internal state which is modelled by a stationary Markov process. First we calculate the limiting diffusion coefficient. Then we show that the ‘active part’ of the diffusion coefficient is in some sense maximal...

Diffusive behaviour and large deviations of one-dimensional active particles with drift

In this thesis a simple model of an active particle was taken, one including a drift according to its internal state. For this model a diffusion coefficient was determined as well as a rate function for the large deviations. This same model is also applied to electrons, although these particles are not active a diffusion coefficient was also...