IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2304.04453.html
   My bibliography  Save this paper

A stochastic control perspective on term structure models with roll-over risk

Author

Listed:
  • Claudio Fontana
  • Simone Pavarana
  • Wolfgang J. Runggaldier

Abstract

In this paper, we consider a generic interest rate market in the presence of roll-over risk, which generates spreads in spot/forward term rates. We do not require classical absence of arbitrage and rely instead on a minimal market viability assumption, which enables us to work in the context of the benchmark approach. In a Markovian setting, we extend the control theoretic approach of Gombani & Runggaldier (2013) and derive representations of spot/forward spreads as value functions of suitable stochastic optimal control problems, formulated under the real-world probability and with power-type objective functionals. We determine endogenously the funding-liquidity spread by relating it to the risk-sensitive optimization problem of a representative investor.

Suggested Citation

  • 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.
    • Handle: RePEc:arx:papers:2304.04453
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2304.04453
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Claudio Fontana & Wolfgang J. Runggaldier, 2012. "Diffusion-based models for financial markets without martingale measures," Papers 1209.4449, arXiv.org, revised Feb 2013.
    2. 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).
    3. Eckhard Platen, 2006. "A Benchmark Approach To Finance," Mathematical Finance, Wiley Blackwell, vol. 16(1), pages 131-151, January.
    4. 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.
    5. Damir Filipović & Eckhard Platen, 2009. "Consistent Market Extensions Under The Benchmark Approach," Mathematical Finance, Wiley Blackwell, vol. 19(1), pages 41-52, January.
    6. Yuri Kabanov & Constantinos Kardaras & Shiqi Song, 2016. "No arbitrage of the first kind and local martingale numéraires," Finance and Stochastics, Springer, vol. 20(4), pages 1097-1108, October.
    7. Tomas Björk & Yuri Kabanov & Wolfgang Runggaldier, 1997. "Bond Market Structure in the Presence of Marked Point Processes," Mathematical Finance, Wiley Blackwell, vol. 7(2), pages 211-239, April.
    8. Huy N. Chau & Andrea Cosso & Claudio Fontana & Oleksii Mostovyi, 2015. "Optimal investment with intermediate consumption under no unbounded profit with bounded risk," Papers 1509.01672, arXiv.org, revised Jun 2017.
    9. Ioannis Karatzas & Constantinos Kardaras, 2007. "The numéraire portfolio in semimartingale financial models," Finance and Stochastics, Springer, vol. 11(4), pages 447-493, October.
    10. Filipović, Damir & Trolle, Anders B., 2013. "The term structure of interbank risk," Journal of Financial Economics, Elsevier, vol. 109(3), pages 707-733.
    11. Gallitschke, Janek & Seifried (née Müller), Stefanie & Seifried, Frank Thomas, 2017. "Interbank interest rates: Funding liquidity risk and XIBOR basis spreads," Journal of Banking & Finance, Elsevier, vol. 78(C), pages 142-152.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    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. Huy N. Chau & Andrea Cosso & Claudio Fontana, 2018. "The value of informational arbitrage," Papers 1804.00442, arXiv.org.
    3. Fontana, Claudio & Runggaldier, Wolfgang J., 2021. "Arbitrage concepts under trading restrictions in discrete-time financial markets," Journal of Mathematical Economics, Elsevier, vol. 92(C), pages 66-80.
    4. Claudio Fontana & Wolfgang J. Runggaldier, 2020. "Arbitrage concepts under trading restrictions in discrete-time financial markets," Papers 2006.15563, arXiv.org, revised Sep 2020.
    5. Eric Jondeau & Benoit Mojon & Jean-Guillaume Sahuc, 2020. "Bank Funding Cost and Liquidity Supply Regimes," BIS Working Papers 854, Bank for International Settlements.
    6. Claudio Fontana, 2015. "Weak And Strong No-Arbitrage Conditions For Continuous Financial Markets," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 18(01), pages 1-34.
    7. Eckhard Platen & Stefan Tappe, 2020. "The Fundamental Theorem of Asset Pricing for Self-Financing Portfolios," Research Paper Series 411, Quantitative Finance Research Centre, University of Technology, Sydney.
    8. Michael Monoyios, 2020. "Infinite horizon utility maximisation from inter-temporal wealth," Papers 2009.00972, arXiv.org, revised Oct 2020.
    9. Tahir Choulli & Sina Yansori, 2018. "Log-optimal portfolio without NFLVR: existence, complete characterization, and duality," Papers 1807.06449, arXiv.org.
    10. Eckhard Platen & Renata Rendek, 2012. "Approximating the numéraire portfolio by naive diversification," Journal of Asset Management, Palgrave Macmillan, vol. 13(1), pages 34-50, February.
    11. Andrea Macrina & Obeid Mahomed, 2018. "Consistent Valuation Across Curves Using Pricing Kernels," Papers 1801.04994, arXiv.org, revised Feb 2018.
    12. Eckhard Platen & Stefan Tappe, 2020. "No arbitrage and multiplicative special semimartingales," Papers 2005.05575, arXiv.org, revised Sep 2022.
    13. Jacopo Mancin & Wolfgang J. Runggaldier, 2015. "On the Existence of Martingale Measures in Jump Diffusion Market Models," Papers 1511.08349, arXiv.org.
    14. Michael Monoyios, 2020. "Duality for optimal consumption under no unbounded profit with bounded risk," Papers 2006.04687, arXiv.org, revised Dec 2021.
    15. Christa Cuchiero & Claudio Fontana & Alessandro Gnoatto, 2019. "Affine multiple yield curve models," Mathematical Finance, Wiley Blackwell, vol. 29(2), pages 568-611, April.
    16. Bálint, Dániel Ágoston, 2022. "Characterisation of L0-boundedness for a general set of processes with no strictly positive element," Stochastic Processes and their Applications, Elsevier, vol. 147(C), pages 51-75.
    17. Eckhard Platen & Renata Rendek, 2017. "Market Efficiency and Growth Optimal Portfolio," Papers 1706.06832, arXiv.org.
    18. Ceci, Claudia & Colaneri, Katia & Cretarola, Alessandra, 2014. "A benchmark approach to risk-minimization under partial information," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 129-146.
    19. Claudio Fontana & Zorana Grbac & Sandrine Gümbel & Thorsten Schmidt, 2020. "Term structure modelling for multiple curves with stochastic discontinuities," Finance and Stochastics, Springer, vol. 24(2), pages 465-511, April.
    20. Andrea Macrina & Obeid Mahomed, 2018. "Consistent Valuation Across Curves Using Pricing Kernels," Risks, MDPI, vol. 6(1), pages 1-39, March.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:2304.04453. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.