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Kriging of financial term-structures

Author

Listed:
  • Areski Cousin

    (SAF - Laboratoire de Sciences Actuarielle et Financière - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon)

  • Hassan Maatouk

    (ENSM ST-ETIENNE - Ecole Nationale Supérieure des Mines de St Etienne, GdR MASCOT-NUM - Méthodes d'Analyse Stochastique des Codes et Traitements Numériques - INSMI-CNRS - Institut National des Sciences Mathématiques et de leurs Interactions - CNRS Mathématiques - CNRS - Centre National de la Recherche Scientifique)

  • Didier Rullière

    (SAF - Laboratoire de Sciences Actuarielle et Financière - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon)

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 Rullière, 2016. "Kriging of financial term-structures," Post-Print hal-01206388, HAL.
    • Handle: RePEc:hal:journl:hal-01206388
    DOI: 10.1016/j.ejor.2016.05.057
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    3. Blomvall, Jörgen & Hagenbjörk, Johan, 2019. "A generic framework for monetary performance attribution," Journal of Banking & Finance, Elsevier, vol. 105(C), pages 121-133.
    4. 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).
    5. Hüttner, Amelie & Scherer, Matthias & Gräler, Benedikt, 2020. "Geostatistical modeling of dependent credit spreads: Estimation of large covariance matrices and imputation of missing data," Journal of Banking & Finance, Elsevier, vol. 118(C).
    6. Realdon, Marco, 2024. "The efficiency of the Estr overnight index swap market," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 91(C).
    7. 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.
    8. 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.
    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. 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.
    12. Damir Filipovi'c & Puneet Pasricha, 2022. "Empirical Asset Pricing via Ensemble Gaussian Process Regression," Papers 2212.01048, arXiv.org.
    13. 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.

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    Keywords

    no-arbitrage constraints; yield curve; Model risk; OIS discount curve; implied default distribution; interest-rate curve; kriging;
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