IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1602.02907.html
   My bibliography  Save this paper

Simulation of volatility modulated Volterra processes using hyperbolic stochastic partial differential equations

Author

Listed:
  • Fred Espen Benth
  • Heidar Eyjolfsson

Abstract

We propose a finite difference scheme to simulate solutions to a certain type of hyperbolic stochastic partial differential equation (HSPDE). These solutions can in turn estimate so called volatility modulated Volterra (VMV) processes and L\'{e}vy semistationary (LSS) processes, which is a class of processes that have been employed to model turbulence, tumor growth and electricity forward and spot prices. We will see that our finite difference scheme converges to the solution of the HSPDE as we take finer and finer partitions for our finite difference scheme in both time and space. Finally, we demonstrate our method with an example from the energy finance literature.

Suggested Citation

  • Fred Espen Benth & Heidar Eyjolfsson, 2016. "Simulation of volatility modulated Volterra processes using hyperbolic stochastic partial differential equations," Papers 1602.02907, arXiv.org.
    • Handle: RePEc:arx:papers:1602.02907
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1602.02907
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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..
    2. Ole E. Barndorff–Nielsen & Fred Espen Benth & Almut E. D. Veraart, 2010. "Ambit processes and stochastic partial differential equations," CREATES Research Papers 2010-17, Department of Economics and Business Economics, Aarhus University.
    3. Ole E. Barndorff-Nielsen & Fred Espen Benth & Almut E. D. Veraart, 2013. "Modelling energy spot prices by volatility modulated L\'{e}vy-driven Volterra processes," Papers 1307.6332, 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. Dennis Schroers, 2024. "Dynamically Consistent Analysis of Realized Covariations in Term Structure Models," Papers 2406.19412, arXiv.org.
    2. Fred Espen Benth & Heidar Eyjolfsson, 2015. "Representation and approximation of ambit fields in Hilbert space," Papers 1509.08272, arXiv.org.
    3. Benth, Fred Espen & Paraschiv, Florentina, 2016. "A Structural Model for Electricity Forward Prices," Working Papers on Finance 1611, University of St. Gallen, School of Finance.
    4. Ignatieva, Katja & Wong, Patrick, 2022. "Modelling high frequency crude oil dynamics using affine and non-affine jump–diffusion models," Energy Economics, Elsevier, vol. 108(C).
    5. Benth, Fred Espen & Rüdiger, Barbara & Süss, Andre, 2018. "Ornstein–Uhlenbeck processes in Hilbert space with non-Gaussian stochastic volatility," Stochastic Processes and their Applications, Elsevier, vol. 128(2), pages 461-486.
    6. Deschatre, Thomas & Féron, Olivier & Gruet, Pierre, 2021. "A survey of electricity spot and futures price models for risk management applications," Energy Economics, Elsevier, vol. 102(C).
    7. Benth, Fred Espen & Koekebakker, Steen, 2015. "Pricing of forwards and other derivatives in cointegrated commodity markets," Energy Economics, Elsevier, vol. 52(PA), pages 104-117.
    8. Benth, Fred Espen & Paraschiv, Florentina, 2018. "A space-time random field model for electricity forward prices," Journal of Banking & Finance, Elsevier, vol. 95(C), pages 203-216.
    9. Fred Espen Benth & Paul Kruhner, 2014. "Representation of infinite dimensional forward price models in commodity markets," Papers 1403.4111, arXiv.org.
    10. Camilla LandÊn, 2000. "Bond pricing in a hidden Markov model of the short rate," Finance and Stochastics, Springer, vol. 4(4), pages 371-389.
    11. Matsumura, Marco & Moreira, Ajax & Vicente, José, 2011. "Forecasting the yield curve with linear factor models," International Review of Financial Analysis, Elsevier, vol. 20(5), pages 237-243.
    12. Lioui, Abraham, 1998. "Currency risk hedging: Futures vs. forward," Journal of Banking & Finance, Elsevier, vol. 22(1), pages 61-81, January.
    13. Lin, Bing-Huei, 1999. "Fitting the term structure of interest rates for Taiwanese government bonds," Journal of Multinational Financial Management, Elsevier, vol. 9(3-4), pages 331-352, November.
    14. 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.
    15. Tucker, A. L. & Wei, J. Z., 1998. "Valuation of LIBOR-Contingent FX options," Journal of International Money and Finance, Elsevier, vol. 17(2), pages 249-277, April.
    16. Chiarella, Carl & Kang, Boda & Nikitopoulos, Christina Sklibosios & Tô, Thuy-Duong, 2013. "Humps in the volatility structure of the crude oil futures market: New evidence," Energy Economics, Elsevier, vol. 40(C), pages 989-1000.
    17. Will Hicks, 2020. "Pseudo-Hermiticity, Martingale Processes and Non-Arbitrage Pricing," Papers 2009.00360, arXiv.org, revised Apr 2021.
    18. Eckhard Platen, 2005. "An Alternative Interest Rate Term Structure Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 8(06), pages 717-735.
    19. Kimmel, Robert L., 2004. "Modeling the term structure of interest rates: A new approach," Journal of Financial Economics, Elsevier, vol. 72(1), pages 143-183, April.
    20. Roberto Baviera, 2017. "Back-of-the-envelope swaptions in a very parsimonious multicurve interest rate model," Papers 1712.06466, arXiv.org.

    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:1602.02907. 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.