Project CEMAPRE internal
| Title | Rough Volatility Models |
| Participants | João Guerra (Principal Investigator), Henrique Guerreiro (Principal Investigator) |
| Summary | Rough 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 (see [1], [2] and [4]). In this project (which started in 2020 and will end in 2024 - 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 years 2021 and 2022, we studied the joint calibration problem of the VIX and SP500 volatility smiles, using the least squares Monte-Carlo method in stochastic Volterra rough volatility models and also explored some machine learning techniques to obtain a robust and flexible method capable of handling the case of non-Markovian volatility of volatility. Moreover , we used an inhomogeneous fractional Ornstein-Uhlenbeck stochastic equation in order to build a regime switching stochastic change of measure for the rBergomi model yielding upward slopping VIX smiles. We calibrated this model to market emprirical data and showed that the calibration obtained was of very good quality (see [3] and [5]). In the year 2024, we will extend the models and methods developed in 2021/2023 to the case where the volatility of the volatility is also rough, from the theoretical and the computational point of views. |