IDEAS home Printed from https://ideas.repec.org/p/ekd/009007/9668.html
   My bibliography  Save this paper

Real World Scenarios for Interest Rates based on the LIBOR Market Model

Author

Listed:
  • Sara Lopes
  • Carlos Vázquez

Abstract

In this article, we present a methodology to simulate the evolution of interest rates under real world probability measure. More precisely, using the multidimensional LIBOR market model and a specification of the market price of risk vector process, we explain how to perform simulations of the real world forward rates in future, using the Euler scheme with Predictor-Corrector. The proposed methodology allows the presence of negative interest rates as currently observed in the markets. We use the multidimensional LIBOR market model and a specification of the market price of risk vector process, we perform simulations of the real world forward rates observed in future, using the Euler scheme with Predictor-Corrector. We allow for negative interest rates as currently observed in the markets. In this article we choose to model a set of key forward Libor rates using the Libor Market Model(LMM) which can be directly observed in the market, guarantees no arbitrage opportunities in interest rate markets and provides more flexibility to capture all possible curve movements. We expect to produce interest rate scenarios coherent with past realizations that can be used in assessment of investment strategies in interest-rate sensitive portfolios for Asset-Liability Management studies and calculations of Economic Capital for Solvency II.

Suggested Citation

  • Sara Lopes & Carlos Vázquez, 2016. "Real World Scenarios for Interest Rates based on the LIBOR Market Model," EcoMod2016 9668, EcoMod.
    • Handle: RePEc:ekd:009007:9668
    as

    Download full text from publisher

    File URL: http://ecomod.net/system/files/sara.lopes_.Real%20World%20Scenarios%20for%20Interest%20Rates%20based%20on%20the%20LIBOR%20Market%20Model_SL_CV.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
    2. Alan Brace & Dariusz G¸atarek & Marek Musiela, 1997. "The Market Model of Interest Rate Dynamics," Mathematical Finance, Wiley Blackwell, vol. 7(2), pages 127-155, April.
    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. Almeida, Thiago Ramos, 2024. "Estimating time-varying factors’ variance in the string-term structure model with stochastic volatility," Research in International Business and Finance, Elsevier, vol. 70(PA).
    2. Bjork, Tomas, 2009. "Arbitrage Theory in Continuous Time," OUP Catalogue, Oxford University Press, edition 3, number 9780199574742.
    3. Frank De Jong & Joost Driessen & Antoon Pelsser, 2001. "Libor Market Models versus Swap Market Models for Pricing Interest Rate Derivatives: An Empirical Analysis," Review of Finance, European Finance Association, vol. 5(3), pages 201-237.
    4. Mohamed Ben Alaya & Ahmed Kebaier & Djibril Sarr, 2024. "Financial Stochastic Models Diffusion: From Risk-Neutral to Real-World Measure," Papers 2409.12783, arXiv.org.
    5. Sorwar, Ghulam & Barone-Adesi, Giovanni & Allegretto, Walter, 2007. "Valuation of derivatives based on single-factor interest rate models," Global Finance Journal, Elsevier, vol. 18(2), pages 251-269.
    6. Samson Assefa, 2007. "Pricing Swaptions and Credit Default Swaptions in the Quadratic Gaussian Factor Model," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 3-2007, January-A.
    7. R.C. Stapleton & Marti G. Subrahmanyam, 1999. "The Term Structure of Interest Rate-Futures Prices," New York University, Leonard N. Stern School Finance Department Working Paper Seires 99-045, New York University, Leonard N. Stern School of Business-.
    8. Fergusson, Kevin, 2020. "Less-Expensive Valuation And Reserving Of Long-Dated Variable Annuities When Interest Rates And Mortality Rates Are Stochastic," ASTIN Bulletin, Cambridge University Press, vol. 50(2), pages 381-417, May.
    9. repec:uts:finphd:40 is not listed on IDEAS
    10. Samuel Chege Maina, 2011. "Credit Risk Modelling in Markovian HJM Term Structure Class of Models with Stochastic Volatility," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 1-2011, January-A.
    11. Lixin Wu & Fan Zhang, 2008. "Fast swaption pricing under the market model with a square-root volatility process," Quantitative Finance, Taylor & Francis Journals, vol. 8(2), pages 163-180.
    12. Werner Hürlimann, 2012. "Valuation of fixed and variable rate mortgages: binomial tree versus analytical approximations," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 35(2), pages 171-202, November.
    13. Suresh M. Sundaresan, 2000. "Continuous‐Time Methods in Finance: A Review and an Assessment," Journal of Finance, American Finance Association, vol. 55(4), pages 1569-1622, August.
    14. Giuseppe Arbia & Michele Di Marcantonio, 2015. "Forecasting Interest Rates Using Geostatistical Techniques," Econometrics, MDPI, vol. 3(4), pages 1-28, November.
    15. Lin, Shih-Kuei & Wang, Shin-Yun & Chen, Carl R. & Xu, Lian-Wen, 2017. "Pricing Range Accrual Interest Rate Swap employing LIBOR market models with jump risks," The North American Journal of Economics and Finance, Elsevier, vol. 42(C), pages 359-373.
    16. Zhanyu Chen & Kai Zhang & Hongbiao Zhao, 2022. "A Skellam market model for loan prime rate options," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 42(3), pages 525-551, March.
    17. Dai, Qiang & Singleton, Kenneth J., 2003. "Fixed-income pricing," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, edition 1, volume 1, chapter 20, pages 1207-1246, Elsevier.
    18. Olivier Guéant, 2016. "The Financial Mathematics of Market Liquidity: From Optimal Execution to Market Making," Post-Print hal-01393136, HAL.
    19. He, Jie-Cao & Hsieh, Chang-Chieh & Huang, Zi-Wei & Lin, Shih-Kuei, 2023. "Valuation of callable range accrual linked to CMS Spread under generalized swap market model," International Review of Financial Analysis, Elsevier, vol. 90(C).
    20. Francois-Éric Racicot & Raymond Théoret, 2006. "Les modèles HJM et LMM revisités," RePAd Working Paper Series UQO-DSA-wp042006, Département des sciences administratives, UQO.
    21. Leo Krippner, 2013. "A tractable framework for zero lower bound Gaussian term structure models," Reserve Bank of New Zealand Discussion Paper Series DP2013/02, Reserve Bank of New Zealand.

    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:ekd:009007:9668. 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: Theresa Leary (email available below). General contact details of provider: https://edirc.repec.org/data/ecomoea.html .

    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.