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Rational multi-curve models with counterparty-risk valuation adjustments

Author

Listed:
  • Stéphane Crépey
  • Andrea Macrina
  • Tuyet Mai Nguyen
  • David Skovmand

Abstract

We develop a multi-curve term structure set-up in which the modelling ingredients are expressed by rational functionals of Markov processes. We calibrate to London Interbank Offer Rate swaptions data and show that a rational two-factor log-normal multi-curve model is sufficient to match market data with accuracy. We elucidate the relationship between the models developed and calibrated under a risk-neutral measure and their consistent equivalence class under the real-world probability measure . The consistent -pricing models are applied to compute the risk exposures which may be required to comply with regulatory obligations. In order to compute counterparty-risk valuation adjustments, such as credit valuation adjustment, we show how default intensity processes with rational form can be derived. We flesh out our study by applying the results to a basis swap contract.

Suggested Citation

  • Stéphane Crépey & Andrea Macrina & Tuyet Mai Nguyen & David Skovmand, 2016. "Rational multi-curve models with counterparty-risk valuation adjustments," Quantitative Finance, Taylor & Francis Journals, vol. 16(6), pages 847-866, June.
    • Handle: RePEc:taf:quantf:v:16:y:2016:i:6:p:847-866
    DOI: 10.1080/14697688.2015.1095348
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    References listed on IDEAS

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    1. Christa Cuchiero & Claudio Fontana & Alessandro Gnoatto, 2016. "A general HJM framework for multiple yield curve modelling," Finance and Stochastics, Springer, vol. 20(2), pages 267-320, April.
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    Cited by:

    1. Henrik Dam & Andrea Macrina & David Skovmand & David Sloth, 2018. "Rational Models for Inflation-Linked Derivatives," Papers 1801.08804, arXiv.org, revised Jul 2020.
    2. Christa Cuchiero & Claudio Fontana & Alessandro Gnoatto, 2019. "Affine multiple yield curve models," Mathematical Finance, Wiley Blackwell, vol. 29(2), pages 568-611, April.
    3. Markus Hess, 2019. "An Arithmetic Pure-Jump Multi-Curve Interest Rate Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(08), pages 1-30, December.
    4. Andrea Macrina & Obeid Mahomed, 2018. "Consistent Valuation Across Curves Using Pricing Kernels," Papers 1801.04994, arXiv.org, revised Feb 2018.
    5. Andrea Macrina & David Skovmand, 2020. "Rational Savings Account Models for Backward-Looking Interest Rate Benchmarks," Risks, MDPI, vol. 8(1), pages 1-18, March.
    6. Andrea Macrina & Obeid Mahomed, 2018. "Consistent Valuation Across Curves Using Pricing Kernels," Risks, MDPI, vol. 6(1), pages 1-39, March.
    7. Yangfan Zhong, 2018. "LIBOR market model with multiplicative basis," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 5(02), pages 1-38, June.
    8. Roberto Baviera, 2019. "Back-Of-The-Envelope Swaptions In A Very Parsimonious Multi-Curve Interest Rate Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(05), pages 1-24, August.
    9. Yangfan Zhong & Yanhui Mi, 2018. "Pricing in-arrears caps and ratchet caps under LIBOR market model with multiplicative basis," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 5(03), pages 1-31, September.

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