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Efficient exposure computation by risk factor decomposition

Author

Listed:
  • Cornelis S. L. de Graaf
  • Drona Kandhai
  • Christoph Reisinger

Abstract

The focus of this paper is the efficient computation of counterparty credit risk exposure on portfolio level. Here, the large number of risk factors rules out traditional PDE-based techniques and allows only a relatively small number of paths for nested Monte Carlo simulations, resulting in large variances of estimators in practice. We propose a novel approach based on Kolmogorov forward and backward PDEs, where we counter the high dimensionality by a generalisation of anchored-ANOVA decompositions. By computing only the most significant terms in the decomposition, the dimensionality is reduced effectively, such that a significant computational speed-up arises from the high accuracy of PDE schemes in low dimensions compared to Monte Carlo estimation. Moreover, we show how this truncated decomposition can be used as control variate for the full high-dimensional model, such that any approximation errors can be corrected while a substantial variance reduction is achieved compared to the standard simulation approach. We investigate the accuracy for a realistic portfolio of exchange options, interest rate and cross-currency swaps under a fully calibrated ten-factor model.

Suggested Citation

  • Cornelis S. L. de Graaf & Drona Kandhai & Christoph Reisinger, 2016. "Efficient exposure computation by risk factor decomposition," Papers 1608.01197, arXiv.org, revised Feb 2018.
  • Handle: RePEc:arx:papers:1608.01197
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    References listed on IDEAS

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    Cited by:

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    3. Kumar, Manish & Kumar, Arun, 2017. "Performance assessment and degradation analysis of solar photovoltaic technologies: A review," Renewable and Sustainable Energy Reviews, Elsevier, vol. 78(C), pages 554-587.
    4. Salvador, Beatriz & Oosterlee, Cornelis W., 2021. "Total value adjustment for a stochastic volatility model. A comparison with the Black–Scholes model," Applied Mathematics and Computation, Elsevier, vol. 391(C).

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