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CDO calibration via Magnus Expansion and Deep Learning

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  • Marco Di Francesco
  • Kevin Kamm

Abstract

In this paper, we improve the performance of the large basket approximation developed by Reisinger et al. to calibrate Collateralized Debt Obligations (CDO) to iTraxx market data. The iTraxx tranches and index are computed using a basket of size $K= 125$. In the context of the large basket approximation, it is assumed that this is sufficiently large to approximate it by a limit SPDE describing the portfolio loss of a basket with size $K\rightarrow \infty$. For the resulting SPDE, we show four different numerical methods and demonstrate how the Magnus expansion can be applied to efficiently solve the large basket SPDE with high accuracy. Moreover, we will calibrate a structural model to the available market data. For this, it is important to efficiently infer the so-called initial distances to default from the Credit Default Swap (CDS) quotes of the constituents of the iTraxx for the large basket approximation. We will show how Deep Learning techniques can help us to improve the performance of this step significantly. We will see in the end a good fit to the market data and develop a highly parallelizable numerical scheme using GPU and multithreading techniques.

Suggested Citation

  • Marco Di Francesco & Kevin Kamm, 2022. "CDO calibration via Magnus Expansion and Deep Learning," Papers 2212.12318, arXiv.org.
    • Handle: RePEc:arx:papers:2212.12318
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    References listed on IDEAS

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    1. Kevin Kamm & Michelle Muniz, 2022. "Rating Triggers for Collateral-Inclusive XVA via Machine Learning and SDEs on Lie Groups," Papers 2211.00326, arXiv.org.
    2. Michael B. Giles & Christoph Reisinger, 2012. "Stochastic finite differences and multilevel Monte Carlo for a class of SPDEs in finance," Papers 1204.1442, arXiv.org.
    3. Conghui Hu & Xun Zhang & Qiuming Gao, 2015. "Synthetic CDO pricing: the perspective of risk integration," Applied Economics, Taylor & Francis Journals, vol. 47(15), pages 1574-1587, March.
    4. Nick Bush & Ben M. Hambly & Helen Haworth & Lei Jin & Christoph Reisinger, 2011. "Stochastic evolution equations in portfolio credit modelling with applications to exotic credit products," Papers 1103.4947, arXiv.org, revised Apr 2011.
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