IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2301.13595.html
   My bibliography  Save this paper

Local Volatility in Interest Rate Models

Author

Listed:
  • V. M. Belyaev

Abstract

Local Volatility (LV) is a very powerful tool for market modeling. This tool can be used to generate arbitrage-free scenarios calibrated to all available options. Here we demonstrate how to implement LV in order to reproduce most swaption prices within a single model. There was a good agreement between market prices and Monte Carlo prices for all tenors and maturities from 2 to 20 years. Note that due to the use of a normal distribution in the scenario generation process, the volatility of short-term swaptions cannot be generated accurately.

Suggested Citation

  • V. M. Belyaev, 2023. "Local Volatility in Interest Rate Models," Papers 2301.13595, arXiv.org, revised Oct 2024.
    • Handle: RePEc:arx:papers:2301.13595
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2301.13595
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Heath, David & Jarrow, Robert & Morton, Andrew, 1990. "Bond Pricing and the Term Structure of Interest Rates: A Discrete Time Approximation," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 25(4), pages 419-440, December.
    2. Viorel Costeanu & Dan Pirjol, 2011. "Asymptotic Expansion for the Normal Implied Volatility in Local Volatility Models," Papers 1105.3359, arXiv.org.
    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. Robert R. Bliss & Ehud I. Ronn, 1997. "Callable U.S. Treasury bonds: optimal calls, anomalies, and implied volatilities," FRB Atlanta Working Paper 97-1, Federal Reserve Bank of Atlanta.
    2. Das, Sanjiv Ranjan, 1998. "A direct discrete-time approach to Poisson-Gaussian bond option pricing in the Heath-Jarrow-Morton model," Journal of Economic Dynamics and Control, Elsevier, vol. 23(3), pages 333-369, November.
    3. Chuang-Chang Chang & Ruey-Jenn Ho & Chengfew Lee, 2010. "Pricing credit card loans with default risks: a discrete-time approach," Review of Quantitative Finance and Accounting, Springer, vol. 34(4), pages 413-438, May.
    4. Rosa Ferrentino & Luca Vota, 2022. "A Mathematical Model for the Pricing of Derivative Financial Products: the Role of the Banking Supervision and of the Model Risk," Journal of Finance and Investment Analysis, SCIENPRESS Ltd, vol. 11(1), pages 1-2.
    5. Glasserman, P. & Zhao, X., 1998. "Arbitrage-Free Discretization of Lognormal Forward Libor and Swap Rate Models," Papers 98-09, Columbia - Graduate School of Business.
    6. 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.
    7. Anja Richter & Josef Teichmann, 2014. "Discrete Time Term Structure Theory and Consistent Recalibration Models," Papers 1409.1830, arXiv.org.
    8. repec:uts:finphd:40 is not listed on IDEAS
    9. Patrick Hagan & Diana Woodward, 1999. "Markov interest rate models," Applied Mathematical Finance, Taylor & Francis Journals, vol. 6(4), pages 233-260.
    10. Kim, Dong H. & Stock, Duane, 2014. "The effect of interest rate volatility and equity volatility on corporate bond yield spreads: A comparison of noncallables and callables," Journal of Corporate Finance, Elsevier, vol. 26(C), pages 20-35.
    11. Oldrich Alfons Vasicek & Francisco Venegas-Martínez, 2021. "Models of the Term Structure of Interest Rates: Review, Trends, and Perspectives," Remef - Revista Mexicana de Economía y Finanzas Nueva Época REMEF (The Mexican Journal of Economics and Finance), Instituto Mexicano de Ejecutivos de Finanzas, IMEF, vol. 16(2), pages 1-28, Abril - J.
    12. Isaiah Hull & Or Sattath & Eleni Diamanti & Göran Wendin, 2024. "Quantum Technology for Economists," Contributions to Economics, Springer, number 978-3-031-50780-9, December.
    13. Dwight Grant & Gautam Vora, 2006. "Extending the universality of the Heath–Jarrow–Morton model," Review of Financial Economics, John Wiley & Sons, vol. 15(2), pages 129-157.
    14. Klaassen, Pieter, 1997. "Discretized reality and spurious profits in stochastic programming models for asset/liability management," Serie Research Memoranda 0011, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
    15. David Bolder, 2001. "Affine Term-Structure Models: Theory and Implementation," Staff Working Papers 01-15, Bank of Canada.
    16. Sanjiv Ranjan Das & Rangarajan K. Sundaram, 1998. "A Direct Approach to Arbitrage-Free Pricing of Derivatives," New York University, Leonard N. Stern School Finance Department Working Paper Seires 99-013, New York University, Leonard N. Stern School of Business-.
    17. Lawrence M. Vielhaber, 2024. "How to Value Proved but Undeveloped Petroleum Reserves," The Energy Journal, , vol. 45(2), pages 23-47, March.
    18. Massimo Costabile & Ivar Massabó & Emilio Russo, 2011. "A binomial approximation for two-state Markovian HJM models," Review of Derivatives Research, Springer, vol. 14(1), pages 37-65, April.
    19. Byers, Joe Wayne, 2006. "Commodity storage valuation: A linear optimization based on traded instruments," Energy Economics, Elsevier, vol. 28(3), pages 275-287, May.
    20. Wilhelm, Jochen, 2000. "Das Gaußsche Zinsstrukturmodell: Eine Analyse auf der Basis von Wahrscheinlichkeitsverteilungen," Passauer Diskussionspapiere, Betriebswirtschaftliche Reihe 6, University of Passau, Faculty of Business and Economics.
    21. Olivier Guéant, 2016. "The Financial Mathematics of Market Liquidity: From Optimal Execution to Market Making," Post-Print hal-01393136, HAL.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:2301.13595. 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.