IDEAS home Printed from https://ideas.repec.org/p/sgh/kaewps/2018038.html
   My bibliography  Save this paper

Markovian and multi-curve friendly parametrisation of HJM model used in valuation adjustment of interest rate derivatives

Author

Listed:
  • Marcin Dec

Abstract

We consider feasible Heath-Jarrow-Morton framework specifications that are easily implementable in XVA engines when pricing linear and non-linear interest rate derivatives in multicurve environment. Our particular focus is on relatively less liquid markets (Polish PLN) and the calibration problems arising from that fact. We first develop necessary tool-kit for multicurve construction and XVA integration and then show and discuss various specifications of HJM model with regard to their practical usage. We demonstrate the importance of Cheyette subclass and derive dynamics of instantaneous forward rates in generic form. We performed calibrations of several one-factor models of that form and found out that even with relatively simple specification i.e. Hull-White with two summands we may achieve satisfactory results in terms of calibration's quality and calculation time.

Suggested Citation

  • Marcin Dec, 2018. "Markovian and multi-curve friendly parametrisation of HJM model used in valuation adjustment of interest rate derivatives," KAE Working Papers 2018-038, Warsaw School of Economics, Collegium of Economic Analysis.
    • Handle: RePEc:sgh:kaewps:2018038
    as

    Download full text from publisher

    File URL: http://kolegia.sgh.waw.pl/pl/KAE/Documents/WorkingPapersKAE/WPKAE_2018_038.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Ingo Beyna & Carl Chiarella & Boda Kang, 2012. "Pricing Interest Rate Derivatives in a Multifactor HJM Model with Time," Research Paper Series 317, Quantitative Finance Research Centre, University of Technology, Sydney.
    2. Beyna, Ingo & Wystup, Uwe, 2010. "On the calibration of the Cheyette interest rate model," CPQF Working Paper Series 25, Frankfurt School of Finance and Management, Centre for Practical Quantitative Finance (CPQF).
    3. N. Moreni & A. Pallavicini, 2014. "Parsimonious HJM modelling for multiple yield curve dynamics," Quantitative Finance, Taylor & Francis Journals, vol. 14(2), pages 199-210, February.
    4. Ingo Beyna, 2013. "Interest Rate Derivatives," Lecture Notes in Economics and Mathematical Systems, Springer, edition 127, number 978-3-642-34925-6, December.
    5. Bianchetti, Marco, 2008. "Two Curves, One Price :Pricing & Hedging Interest Rate Derivatives Decoupling Forwarding and Discounting Yield Curves," MPRA Paper 22022, University Library of Munich, Germany, revised 24 Jan 2010.
    6. Marco Bianchetti & Mattia Carlicchi, 2011. "Interest Rates After The Credit Crunch: Multiple-Curve Vanilla Derivatives and SABR," Papers 1103.2567, arXiv.org, revised Apr 2012.
    7. Marc Henrard, 2003. "Explicit bond option and swaption formula in Heath-Jarrow-Morton one factor model," Finance 0310009, University Library of Munich, Germany.
    8. David Heath & Robert Jarrow & Andrew Morton, 2008. "Bond Pricing And The Term Structure Of Interest Rates: A New Methodology For Contingent Claims Valuation," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 13, pages 277-305, World Scientific Publishing Co. Pte. Ltd..
    9. Patrick Hagan & Graeme West, 2006. "Interpolation Methods for Curve Construction," Applied Mathematical Finance, Taylor & Francis Journals, vol. 13(2), pages 89-129.
    10. Ho, Thomas S Y & Lee, Sang-bin, 1986. "Term Structure Movements and Pricing Interest Rate Contingent Claims," Journal of Finance, American Finance Association, vol. 41(5), pages 1011-1029, December.
    11. Peter Ritchken & L. Sankarasubramanian, 1995. "Volatility Structures Of Forward Rates And The Dynamics Of The Term Structure1," Mathematical Finance, Wiley Blackwell, vol. 5(1), pages 55-72, January.
    12. Marc Henrard, 2003. "Explicit Bond Option Formula In Heath–Jarrow–Morton One Factor Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 6(01), pages 57-72.
    13. Alan Brace & Marek Musiela, 1994. "A Multifactor Gauss Markov Implementation Of Heath, Jarrow, And Morton," Mathematical Finance, Wiley Blackwell, vol. 4(3), pages 259-283, July.
    14. Marco Bianchetti, 2009. "Two Curves, One Price: Pricing & Hedging Interest Rate Derivatives Decoupling Forwarding and Discounting Yield Curves," Papers 0905.2770, arXiv.org, revised Jul 2012.
    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. Chiara Sabelli & Michele Pioppi & Luca Sitzia & Giacomo Bormetti, 2014. "Multi-curve HJM modelling for risk management," Papers 1411.3977, arXiv.org, revised Oct 2015.
    2. Bjork, Tomas, 2009. "Arbitrage Theory in Continuous Time," OUP Catalogue, Oxford University Press, edition 3, number 9780199574742.
    3. Chiarella, Carl & Clewlow, Les & Musti, Silvana, 2005. "A volatility decomposition control variate technique for Monte Carlo simulations of Heath Jarrow Morton models," European Journal of Operational Research, Elsevier, vol. 161(2), pages 325-336, March.
    4. Camilla Landén & Tomas Björk, 2002. "On the construction of finite dimensional realizations for nonlinear forward rate models," Finance and Stochastics, Springer, vol. 6(3), pages 303-331.
    5. Ingo Beyna, 2013. "Interest Rate Derivatives," Lecture Notes in Economics and Mathematical Systems, Springer, edition 127, number 978-3-642-34925-6, December.
    6. Björk, Tomas, 2003. "On the Geometry of Interest Rate Models," SSE/EFI Working Paper Series in Economics and Finance 545, Stockholm School of Economics.
    7. Carl Chiarella & Xue-Zhong He & Christina Sklibosios Nikitopoulos, 2015. "Derivative Security Pricing," Dynamic Modeling and Econometrics in Economics and Finance, Springer, edition 127, number 978-3-662-45906-5, July-Dece.
    8. Ingo Beyna & Carl Chiarella & Boda Kang, 2012. "Pricing Interest Rate Derivatives in a Multifactor HJM Model with Time," Research Paper Series 317, Quantitative Finance Research Centre, University of Technology, Sydney.
    9. 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.
    10. R. Bhar & C. Chiarella, 1997. "Transformation of Heath?Jarrow?Morton models to Markovian systems," The European Journal of Finance, Taylor & Francis Journals, vol. 3(1), pages 1-26, March.
    11. Carl Chiarella & Oh-Kang Kwon, 2001. "State Variables and the Affine Nature of Markovian HJM Term Structure Models," Research Paper Series 52, Quantitative Finance Research Centre, University of Technology, Sydney.
    12. Li, Haitao & Ye, Xiaoxia & Yu, Fan, 2020. "Unifying Gaussian dynamic term structure models from a Heath–Jarrow–Morton perspective," European Journal of Operational Research, Elsevier, vol. 286(3), pages 1153-1167.
    13. Giuseppe Arbia & Michele Di Marcantonio, 2015. "Forecasting Interest Rates Using Geostatistical Techniques," Econometrics, MDPI, vol. 3(4), pages 1-28, November.
    14. Flavio Angelini & Stefano Herzel, 2006. "Notes and Comments: An approximation of caplet implied volatilities in Gaussian models," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 28(2), pages 113-127, February.
    15. Gibson, Rajna & Lhabitant, Francois-Serge & Talay, Denis, 2010. "Modeling the Term Structure of Interest Rates: A Review of the Literature," Foundations and Trends(R) in Finance, now publishers, vol. 5(1–2), pages 1-156, December.
    16. Björk, Tomas & Landén, Camilla & Svensson, Lars, 2002. "Finite dimensional Markovian realizations for stochastic volatility forward rate models," SSE/EFI Working Paper Series in Economics and Finance 498, Stockholm School of Economics, revised 07 May 2002.
    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. Bueno-Guerrero, Alberto & Moreno, Manuel & Navas, Javier F., 2016. "The stochastic string model as a unifying theory of the term structure of interest rates," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 461(C), pages 217-237.
    19. Carl Chiarella & Oh Kang Kwon, 2001. "Forward rate dependent Markovian transformations of the Heath-Jarrow-Morton term structure model," Finance and Stochastics, Springer, vol. 5(2), pages 237-257.
    20. Anders B. Trolle & Eduardo S. Schwartz, 2009. "A General Stochastic Volatility Model for the Pricing of Interest Rate Derivatives," The Review of Financial Studies, Society for Financial Studies, vol. 22(5), pages 2007-2057, May.

    More about this item

    Keywords

    instantaneous forward rate models; multi-curve valuation; valuation adjustments; XVA; Heath-Jarrow-Morton; volatility surface calibration; HJM framework; Monte Carlo simulation; Cheyette model; Gaussian models;
    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
    • E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Interest Rates: Determination, Term Structure, and Effects

    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:sgh:kaewps:2018038. 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: Dariusz Nojszewski (email available below). General contact details of provider: https://edirc.repec.org/data/kawawpl.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.