Calibrating Multivariate Lévy Processes with Neural Networks

Kailai Xu, Eric Darve
Proceedings of The First Mathematical and Scientific Machine Learning Conference, PMLR 107:207-220, 2020.

Abstract

Calibrating a Lévy process usually requires characterizing its jump distribution. Traditionally this problem can be solved with nonparametric estimation using the empirical characteristic functions (ECF), assuming certain regularity, and results to date are mostly in 1D. For multivariate Lévy processes and less smooth Lévy densities, the problem becomes challenging as ECFs decay slowly and have large uncertainty because of limited observations. We solve this problem by approximating the Lévy density with a parametrized functional form; the characteristic function is then estimated using numerical integration. In our benchmarks, we used deep neural networks and found that they are robust and can capture sharp transitions in the Lévy density compared to piecewise linear functions and radial basis functions.

Cite this Paper

BibTeX
@InProceedings{pmlr-v107-xu20a, title = {Calibrating Multivariate {L}évy Processes with Neural Networks}, author = {Xu, Kailai and Darve, Eric}, booktitle = {Proceedings of The First Mathematical and Scientific Machine Learning Conference}, pages = {207--220}, year = {2020}, editor = {Lu, Jianfeng and Ward, Rachel}, volume = {107}, series = {Proceedings of Machine Learning Research}, month = {20--24 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v107/xu20a/xu20a.pdf}, url = {https://proceedings.mlr.press/v107/xu20a.html}, abstract = { Calibrating a Lévy process usually requires characterizing its jump distribution. Traditionally this problem can be solved with nonparametric estimation using the empirical characteristic functions (ECF), assuming certain regularity, and results to date are mostly in 1D. For multivariate Lévy processes and less smooth Lévy densities, the problem becomes challenging as ECFs decay slowly and have large uncertainty because of limited observations. We solve this problem by approximating the Lévy density with a parametrized functional form; the characteristic function is then estimated using numerical integration. In our benchmarks, we used deep neural networks and found that they are robust and can capture sharp transitions in the Lévy density compared to piecewise linear functions and radial basis functions. } }
Endnote
%0 Conference Paper %T Calibrating Multivariate Lévy Processes with Neural Networks %A Kailai Xu %A Eric Darve %B Proceedings of The First Mathematical and Scientific Machine Learning Conference %C Proceedings of Machine Learning Research %D 2020 %E Jianfeng Lu %E Rachel Ward %F pmlr-v107-xu20a %I PMLR %P 207--220 %U https://proceedings.mlr.press/v107/xu20a.html %V 107 %X Calibrating a Lévy process usually requires characterizing its jump distribution. Traditionally this problem can be solved with nonparametric estimation using the empirical characteristic functions (ECF), assuming certain regularity, and results to date are mostly in 1D. For multivariate Lévy processes and less smooth Lévy densities, the problem becomes challenging as ECFs decay slowly and have large uncertainty because of limited observations. We solve this problem by approximating the Lévy density with a parametrized functional form; the characteristic function is then estimated using numerical integration. In our benchmarks, we used deep neural networks and found that they are robust and can capture sharp transitions in the Lévy density compared to piecewise linear functions and radial basis functions.
APA
Xu, K. & Darve, E.. (2020). Calibrating Multivariate Lévy Processes with Neural Networks. Proceedings of The First Mathematical and Scientific Machine Learning Conference, in Proceedings of Machine Learning Research 107:207-220 Available from https://proceedings.mlr.press/v107/xu20a.html.

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