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Kriging of financial term-structures

Author

Listed:
  • Areski Cousin

    (SAF)

  • Hassan Maatouk

    (GdR MASCOT-NUM, LIMOS, DEMO-ENSMSE)

  • Didier Rulli`ere

    (SAF)

Abstract
Due to the lack of reliable market information, building financial term-structures may be associated with a significant degree of uncertainty. In this paper, we propose a new term-structure interpolation method that extends classical spline techniques by additionally allowing for quantification of uncertainty. The proposed method is based on a generalization of kriging models with linear equality constraints (market-fit conditions) and shape-preserving conditions such as monotonicity or positivity (no-arbitrage conditions). We define the most likely curve and show how to build confidence bands. The Gaussian process covariance hyper-parameters under the construction constraints are estimated using cross-validation techniques. Based on observed market quotes at different dates, we demonstrate the efficiency of the method by building curves together with confidence intervals for term-structures of OIS discount rates, of zero-coupon swaps rates and of CDS implied default probabilities. We also show how to construct interest-rate surfaces or default probability surfaces by considering time (quotation dates) as an additional dimension.

Suggested Citation

  • Areski Cousin & Hassan Maatouk & Didier Rulli`ere, 2016. "Kriging of financial term-structures," Papers 1604.02237, arXiv.org.
    • Handle: RePEc:arx:papers:1604.02237
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    3. Stéphane Crépey & Matthew F Dixon, 2020. "Gaussian process regression for derivative portfolio modeling and application to credit valuation adjustment computations," Post-Print hal-03910109, HAL.
    4. Damir Filipovi'c & Puneet Pasricha, 2022. "Empirical Asset Pricing via Ensemble Gaussian Process Regression," Papers 2212.01048, arXiv.org.
    5. Hainaut, Donatien, 2021. "Lévy interest rate models with a long memory," LIDAM Discussion Papers ISBA 2021020, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    6. Johan Hagenbjörk & Jörgen Blomvall, 2019. "Simulation and evaluation of the distribution of interest rate risk," Computational Management Science, Springer, vol. 16(1), pages 297-327, February.
    7. St'ephane Cr'epey & Matthew Dixon, 2019. "Gaussian Process Regression for Derivative Portfolio Modeling and Application to CVA Computations," Papers 1901.11081, arXiv.org, revised Oct 2019.
    8. Djibril Gueye & Kokulo Lawuobahsumo, 2023. "A Probabilistic Approach for Denoising Option Prices," International Journal of Economics and Financial Issues, Econjournals, vol. 13(2), pages 18-26, March.
    9. Kapusuzoglu, Berkcan & Mahadevan, Sankaran, 2021. "Information fusion and machine learning for sensitivity analysis using physics knowledge and experimental data," Reliability Engineering and System Safety, Elsevier, vol. 214(C).
    10. Rabitti, Giovanni & Borgonovo, Emanuele, 2020. "Is mortality or interest rate the most important risk in annuity models? A comparison of sensitivity analysis methods," Insurance: Mathematics and Economics, Elsevier, vol. 95(C), pages 48-58.
    11. Blomvall, Jörgen & Hagenbjörk, Johan, 2019. "A generic framework for monetary performance attribution," Journal of Banking & Finance, Elsevier, vol. 105(C), pages 121-133.
    12. Marc Chataigner & Areski Cousin & St'ephane Cr'epey & Matthew Dixon & Djibril Gueye, 2022. "Beyond Surrogate Modeling: Learning the Local Volatility Via Shape Constraints," Papers 2212.09957, arXiv.org.
    13. Realdon, Marco, 2024. "The efficiency of the Estr overnight index swap market," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 91(C).

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