Stationary Heston model: calibration and pricing of exotics using product recursive quantization

Abstract

Product Recursive Quantization is used to price exotic options in the Stationary Heston model, a model that generates more realistic volatility surfaces than the original Heston model

Acknowledgments

The authors wish to thank Guillaume Aubert for fruitful discussion on the Heston model and Jean-Michel Fayolle for his advice on the calibration of the models. The PhD thesis of Thibaut Montes is funded by a CIFRE grant from The Independent Calculation Agent (The ICA) and French ANRT. The first and third authors benefited for the support of the ‘Chaire Risques financiers’ funded by the Société Générale, under the aegis of the Fondation du Risque.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 In practice, we choose n = 20. This number of points allows us to reach a high precision while keeping the computation time under control.

2 During our numerical tests, we used the numerical integration routine gsl$\mathrm{\_}$integration$\mathrm{\_}$fixed$\mathrm{\_}$laguerre developed in the C++ gsl library. See https://www.gnu.org/software/gsl/doc/html/integration.html for more details on the implementation.

3 C++ implementation of the upper right tail of a bivariate normal distribution can be found in John Burkardt's website: https://people.sc.fsu.edu/jburkardt/cpp_src/toms462/toms462.html.

4 All the numerical tests have been carried out in C++ on a laptop with a 2,4 GHz 8-Core Intel Core i9 CPU. The computations of the transition probabilities are parallelized on the CPU.

Additional information

Funding

This work was supported by Association Nationale de la Recherche (ANR) [2016/1360] ‘Chaire Risques Financiers’ funded by Société Générale, under the aegis of ‘Fondation du Risque’ [N/A].