sigsde_calibration

This is a collection of Jupyter notebooks and Python files which have been used in the article:

"Signature-based models: theory and calibration"

of Christa Cuchiero, Guido Gazzani and Sara Svaluto-Ferro.

For citations:
MDPI and ACS Style
Cuchiero, C.; Gazzani, G.; Svaluto-Ferro, S. Signature-based models: theory and calibration.

@article{CGS:22,
  author = {Cuchiero, C. and Gazzani, G. and Svaluto-Ferro, S.},
title = {Signature-Based Models: Theory and Calibration},
journal = {SIAM Journal on Financial Mathematics},
volume = {14},
number = {3},
pages = {910-957},
year = {2023}
}

In the present repository you will find the following material.

Calibration to time-series data

• Code for a Heston model, when learning the price dynamics. (Stoch_vol_regressionPrice_Heston.py)


• Code for a SABR-type model, when learning the volatility of the price dynamics. (Stoch_vol_regressionQV_SABR.py)

Details of the calibration to time-series data with signature-based model can be found in Section 4.1 of the paper.

Calibration to option prices

• Code for a Heston model generated implied volatility surface with constant model parameters.(MC_Heston.ipynb)


• Code for market-data with constant parameters.(MC_market_calibration.ipynb)


• Code for a market-data with time-varying parameters. (Cluster_MC_Time_Varying.py ran on the UniWien HPC3 Cluster and the corresponding notebook to visualize the results Calibration_TimeVarying.ipynb)

Details of the calibration to option prices with signature-based model can be found in Section 4.2 of the paper.

Joint calibration to time-series data and option prices

• Code for a Heston model with constant parameters. (Joint_Calibration.py)

A brief discussion concerning the joint calibration problem can be found in Section 4.3 of the paper.