publications
2025
- JournalLong time asymptotic behavior of a self-similar fragmentation equationGaetano Agazzotti, Madalina Deaconu, and Antoine LejayNonlinear Analysis, 2025
Using the Mellin transform, we study self-similar fragmentation equations whose breakage rate follows the power law distribution, and a particle is split into a fixed number of smaller particles. First, we show how to extend the solution of such equations to measure-valued initial conditions, by a closure argument on the Mellin space. Second, we use appropriate series representations to give a rigorous proof to the asymptotic behavior of the moments, completing some results known through heuristic derivations.
@article{agazzotti2024long, title = {Long time asymptotic behavior of a self-similar fragmentation equation}, journal = {Nonlinear Analysis}, volume = {257}, pages = {113805}, year = {2025}, issn = {0362-546X}, doi = {https://doi.org/10.1016/j.na.2025.113805}, url = {https://www.sciencedirect.com/science/article/pii/S0362546X25000598}, author = {Agazzotti, Gaetano and Deaconu, Madalina and Lejay, Antoine}, keywords = {Self-similar fragmentation, Mellin transform, Measure-valued equation, Moments problem, Series expansion}, } - JournalCalibration and option pricing with stochastic volatility and double exponential jumpsGaetano Agazzotti, Jean-Philippe Aguilar, Claudio Aglieri Rinella, and 1 more authorJournal of Computational and Applied Mathematics, 2025
This work examines a stochastic volatility model with double-exponential jumps in the context of option pricing. The model has been considered in previous research articles, but no thorough analysis had been conducted to study its quality of calibration and pricing capabilities thus far. We provide evidence that this model outperforms challenger models possessing similar features (stochastic volatility and jumps), especially in the fit of the short term implied volatility smile, and that it is particularly tractable for the pricing of exotic options from different generations. The article utilizes Fourier pricing techniques (the PROJ method and its refinements) for different types of claims and several generations of exotics (Asian options, cliquets, barrier options, and options on realized variance), and all source codes are made publicly available to facilitate adoption and future research. The results indicate that this model is highly promising, thanks to the asymmetry of the jumps distribution allowing it to capture richer dynamics than a normal jump size distribution. The parameters all have meaningful econometrics interpretations that are important for adoption by risk-managers.
@article{agazzotti225hkde, title = {Calibration and option pricing with stochastic volatility and double exponential jumps}, journal = {Journal of Computational and Applied Mathematics}, volume = {465}, pages = {116563}, year = {2025}, issn = {0377-0427}, doi = {https://doi.org/10.1016/j.cam.2025.116563}, url = {https://www.sciencedirect.com/science/article/pii/S0377042725000780}, author = {Agazzotti, Gaetano and Aguilar, Jean-Philippe and {Aglieri Rinella}, Claudio and Kirkby, Justin Lars}, keywords = {Calibration, Option pricing, Heston model, Jump diffusion, Stochastic volatility models, Exotic options, Volatility surface, Double exponential distribution}, }
2024
- PreprintThe bilateral generalized inverse Gaussian process with applications to financial modelingGaetano Agazzotti, and Jean-Philippe Aguilar2024
We introduce and document a class of probability distributions, called bilateral generalized inverse Gaussian (BGIG) distributions, that are obtained by convolution of two generalized inverse Gaussian distributions supported by the positive and negative semi-axis. We prove several results regarding their analyticity, shapes and asymptotics, and we introduce the associated Lévy processes as well as their main properties. We study the behaviour of these processes under change of measure, their simulations and the structure of their sample paths, and we introduce a stock market model constructed by means of exponential BGIG processes. Based on real market data, we show that this model is easy to calibrate thanks notably to idiosyncratic properties of BGIG distributions, and that it is well suited to Monte Carlo and Fourier option pricing.
@misc{agazzotti2024bgig, title = {The bilateral generalized inverse Gaussian process with applications to financial modeling}, author = {Agazzotti, Gaetano and Aguilar, Jean-Philippe}, year = {2024}, eprint = {2407.10557}, archiveprefix = {arXiv}, primaryclass = {math.PR}, url = {https://arxiv.org/abs/2407.10557}, }
2023
- ConferenceDeep Image Prior Regularized by Coupled Total Variation for Image ColorizationGaetano Agazzotti, Fabien Pierre, and Frédéric SurIn Scale Space and Variational Methods in Computer Vision, 2023
Automatic image colorization is an old problem in image processing that has regained interest in the recent years with the emergence of deep-learning approaches with dramatic results. A careful examination shows that these methods often suffer from the so-called “color halos” or “color bleeding” effect: some colors are not well localized and may cross shape edges. This phenomenon is caused by the non-alignment of edges in the luminance and chrominance maps. We address this problem by regularizing the output of an efficient image colorization method with deep image prior and coupled total variation.
@inproceedings{agazzotti2023dipctv, author = {Agazzotti, Gaetano and Pierre, Fabien and Sur, Fr{\'e}d{\'e}ric}, editor = {Calatroni, Luca and Donatelli, Marco and Morigi, Serena and Prato, Marco and Santacesaria, Matteo}, title = {Deep Image Prior Regularized by Coupled Total Variation for Image Colorization}, booktitle = {Scale Space and Variational Methods in Computer Vision}, year = {2023}, publisher = {Springer International Publishing}, address = {Cham}, pages = {301--313}, isbn = {978-3-031-31975-4}, doi = {https://doi.org/10.1007/978-3-031-31975-4_23}, url = {https://link.springer.com/chapter/10.1007/978-3-031-31975-4_23}, }