Research projects

Project CEMAPRE internal

TitleRough volatility models - numerical methods and stochastic change of measures
ParticipantsJoão Guerra (Principal Investigator), Henrique Guerreiro
SummaryRough volatility models are stochastic volatility models where the log-volatility behaves similarly
to a fBm with H < 1/2. These models are consistent with empirical data, but reproducing the "smile"
effect associated to options on the volatility index VIX remains a challenge.

In this project (which started in 2020 and will end in 2023 - is a project associated to the PhD
thesis of Henrique Guerreiro), the main goals are:
1) Develop numerical methods for the evaluation of option prices and calibration of rough volatility
models, using Monte-Carlo simulations, where we will use variance reduction methods and machine
learning methods in order to improve the computational efficiency.
2) Generalize the rough volatility models by introducing an extra stochastic factor or stochastic
change of measure in order to capture this "smile" effect.

In the year 2021, we have:
(i) Implemented numerical methods for the simulation of the VIX index, option pricing and volatility
curves using nested Monte-Carlo methods and least squares Monte-Carlo methods powered by machine
(ii) used the fractional Ornstein-Uhlenbeck processes to build a stochastic change of measure for
the rBergomi model.

In the year 2022, we will explore the joint calibration problem of the VIX and SP500 volatility
smiles, using the least squares Monte-Carlo method and we will study a generalized rBergomi model
with a stochastic change of measure.