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A consistent stochastic model of the term structure of interest rates for multiple tenors

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  • Alfeus, Mesias
  • Grasselli, Martino
  • Schlögl, Erik

Abstract

Starting from the observation that single-currency swap basis spreads contradict classical arbitrage arguments, we construct a framework where this basis arises due to the presence of “roll-over risk.” This risk consists of two components: (1) facing a higher credit spread (e.g. due to a credit downgrade) when rolling over short-term borrowing (2) heightened borrowing costs due to an absence of market liquidity. The model simultaneously fits OIS, interest rate swap and basis swap market quotes. Including CDS market quotes allows the two components of roll-over risk to be explicitly separated. This is highly relevant to the current LIBOR transition, illustrating why alternative benchmarks are fundamentally different from the rates they may be replacing.

Suggested Citation

  • Alfeus, Mesias & Grasselli, Martino & Schlögl, Erik, 2020. "A consistent stochastic model of the term structure of interest rates for multiple tenors," Journal of Economic Dynamics and Control, Elsevier, vol. 114(C).
    • Handle: RePEc:eee:dyncon:v:114:y:2020:i:c:s0165188920300312
    DOI: 10.1016/j.jedc.2020.103861
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    Cited by:

    1. Claudio Fontana & Simone Pavarana & Wolfgang J. Runggaldier, 2023. "A stochastic control perspective on term structure models with roll-over risk," Finance and Stochastics, Springer, vol. 27(4), pages 903-932, October.
    2. Mesias Alfeus, 2019. "Stochastic Modelling of New Phenomena in Financial Markets," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 1-2019, January-A.
    3. David Skovmand & Jacob Bjerre Skov, 2022. "Decomposing LIBOR in Transition: Evidence from the Futures Markets," Papers 2201.06930, arXiv.org, revised Mar 2022.
    4. Backwell, Alex & Hayes, Joshua, 2022. "Expected and Unexpected Jumps in the Overnight Rate: Consistent Management of the Libor Transition," Journal of Banking & Finance, Elsevier, vol. 145(C).
    5. Andrea Macrina & Obeid Mahomed, 2018. "Consistent Valuation Across Curves Using Pricing Kernels," Papers 1801.04994, arXiv.org, revised Feb 2018.
    6. Andrea Macrina & David Skovmand, 2020. "Rational Savings Account Models for Backward-Looking Interest Rate Benchmarks," Risks, MDPI, vol. 8(1), pages 1-18, March.
    7. Marek Rutkowski & Matthew Bickersteth, 2021. "Pricing and Hedging of SOFR Derivatives under Differential Funding Costs and Collateralization," Papers 2112.14033, arXiv.org.
    8. repec:uts:finphd:41 is not listed on IDEAS
    9. Claudio Fontana & Simone Pavarana & Wolfgang J. Runggaldier, 2023. "A stochastic control perspective on term structure models with roll-over risk," Papers 2304.04453, arXiv.org, revised Oct 2023.
    10. Karol Gellert & Erik Schlogl, 2021. "Short Rate Dynamics: A Fed Funds and SOFR perspective," Papers 2101.04308, arXiv.org.
    11. Eric Jondeau & Benoit Mojon & Jean-Guillaume Sahuc, 2020. "Bank Funding Cost and Liquidity Supply Regimes," BIS Working Papers 854, Bank for International Settlements.
    12. Belssing Taruvinga, 2019. "Solving Selected Problems on American Option Pricing with the Method of Lines," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 4-2019, January-A.
    13. Andrea Macrina & Obeid Mahomed, 2018. "Consistent Valuation Across Curves Using Pricing Kernels," Risks, MDPI, vol. 6(1), pages 1-39, March.
    14. Mesias Alfeus & Erik Schlögl, 2019. "On Spread Option Pricing Using Two-Dimensional Fourier Transform," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(05), pages 1-20, August.
    15. Mesias Alfeus & Erik Schlögl, 2018. "On Numerical Methods for Spread Options," Research Paper Series 388, Quantitative Finance Research Centre, University of Technology, Sydney.
    16. Boda Kang & Christina Nikitopoulos Sklibosios & Erik Schlogl & Blessing Taruvinga, 2019. "The Impact of Jumps on American Option Pricing: The S&P 100 Options Case," Research Paper Series 397, Quantitative Finance Research Centre, University of Technology, Sydney.
    17. Alan Brace & Karol Gellert & Erik Schlögl, 2024. "SOFR term structure dynamics—Discontinuous short rates and stochastic volatility forward rates," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 44(6), pages 936-985, June.

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    More about this item

    Keywords

    Tenor swap; Basis; Frequency basis; Liquidity risk; Swap market; LIBOR/OIS spread;
    All these keywords.

    JEL classification:

    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • G1 - Financial Economics - - General Financial Markets
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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