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A Linear-Rational Multi-Curve Term Structure Model with Stochastic Spread

Author

Listed:
  • José da Fonseca

    (AUT - Auckland University of Technology)

  • Edem Dawui

    (UP1 - Université Paris 1 Panthéon-Sorbonne, PRISM Sorbonne - Pôle de recherche interdisciplinaire en sciences du management - UP1 - Université Paris 1 Panthéon-Sorbonne)

  • Yannick Malevergne

    (UP1 - Université Paris 1 Panthéon-Sorbonne, PRISM Sorbonne - Pôle de recherche interdisciplinaire en sciences du management - UP1 - Université Paris 1 Panthéon-Sorbonne)

Abstract

This study develops a linear-rational multi-curve term structure model based on the Wishart affine process. The model allows for a stochastic correlation between the curves whilst the pricing of swaptions remains at part in terms of numerical complexity with caps and floors. We also show how the constant maturity swap (CMS) and the CMS spread option can be priced. We provide swaption and CMS spread option price approximations that are fast to evaluate and accurate. These approximations heavily rely on the affine property of the Wishart process. We illustrate how the model performs on real data by rolling a calibration using a 3-month long sample of at-the-money swaption data. We find that the estimated parameters are remarkably stable and the calibration procedure is robust. In particular, thanks to the specific Wishart properties the model can handle the stochastic correlation between the OIS term structure and the Euribor-OIS spread term structure.

Suggested Citation

  • José da Fonseca & Edem Dawui & Yannick Malevergne, 2023. "A Linear-Rational Multi-Curve Term Structure Model with Stochastic Spread," Working Papers hal-04012277, HAL.
    • Handle: RePEc:hal:wpaper:hal-04012277
    DOI: 10.2139/ssrn.4176102
    as

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    Keywords

    Interest rate model; Multi-Curve; Wishart process; Stochastic spread; Swaption market; CMS derivatives;
    All these keywords.

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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