RoughVolatility

Implementation of generalized Bergomi model with regime switching market price of volatility risk

This code models the forward variance process where variance is given by $$V_u = \mathbb{E}\left[V_u\mid\mathcal{F}_t\right]\mathcal{E}\left(\eta(K*\eta dW)(u)\right),$$ under a regime swiching market price of volatility risk given by $$\lambda_s=\theta(\mu_s-X_s)$$ where $X$ is a affine volterra type Ornstein-Uhlenbeck process with mean reversion towards $\mu$ goverend by a Markov Chain. For an introduction see [1] or the pdf in /material

For now only the fractional kernel is implemented.

There are main files for estimation in the direct simulation and study of moment error with an approximate simulation of the VIX. Some initial running tests are in /tests.

Setup and requirements

Doing the following should make the code run smoothly on Linux. $PATH$ is the directory that RoughVolatility is in.

python -m venv env

echo "export PYTHONPATH=$PATH$" >> .env

printf "\n# Adding this command to read local .env file" >> env/bin/activate
printf "\nexport \$(grep -v '^#' .env | xargs)" >> env/bin/activate

. env/bin/activate

pip install -r requirements.txt

Manually imported in the code is the Mittag-Leffler function by K. Hinsen[2].

References

[1]: Guerreiro, H. and Guerra, J. (2022). ”VIX pricing in the rBergomi model under a regime switching change of measure”, https://arxiv.org/pdf/2201.10391.pdf.

[2]: Hinsen, K. (2017). ”The Mittag-Leffler function in Python”, https://github.com/ khinsen/mittag-leffler.