IDEAS home Printed from https://ideas.repec.org/p/hal/cesptp/hal-03018478.html
   My bibliography  Save this paper

Sabr Type Stochastic Volatility Operator In Hilbert Space

Author

Listed:
  • Raphaël Douady

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, SUNY - State University of New York)

  • Zeyu Cao

    (SUNY - State University of New York)

Abstract

In this paper, we define stochastic volatility operators in Hilbert space which are analogs to the widely-used SABR model [14] in finite dimensional case. We show the existence of the mild solution and some related regularity properties. Our proof is based on Leray-Schauder fixed point theorem and some priori inequalities on the stochastic operator processes we construct.

Suggested Citation

  • Raphaël Douady & Zeyu Cao, 2020. "Sabr Type Stochastic Volatility Operator In Hilbert Space," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-03018478, HAL.
    • Handle: RePEc:hal:cesptp:hal-03018478
    Note: View the original document on HAL open archive server: https://paris1.hal.science/hal-03018478
    as

    Download full text from publisher

    File URL: https://paris1.hal.science/hal-03018478/document
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. D. P. Kennedy, 1994. "The Term Structure Of Interest Rates As A Gaussian Random Field," Mathematical Finance, Wiley Blackwell, vol. 4(3), pages 247-258, July.
    2. Raphaël Douady, 2013. "Yield Curve Smoothing and Residual Variance of Fixed Income Positions," Post-Print hal-00666751, HAL.
    3. Rama Cont, 2005. "Modeling Term Structure Dynamics: An Infinite Dimensional Approach," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 8(03), pages 357-380.
    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. Bueno-Guerrero, Alberto & Moreno, Manuel & Navas, Javier F., 2015. "Stochastic string models with continuous semimartingales," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 433(C), pages 229-246.
    2. Raphaël Douady, 2013. "Yield Curve Smoothing and Residual Variance of Fixed Income Positions," Post-Print hal-00666751, HAL.
    3. Lijun Bo & Ying Jiao & Xuewei Yang, 2011. "Credit derivatives pricing with default density term structure modelled by L\'evy random fields," Papers 1112.2952, arXiv.org.
    4. Brace, Alan & Fabbri, Giorgio & Goldys, Benjamin, 2007. "An Hilbert space approach for a class of arbitrage free implied volatilities models," MPRA Paper 6321, University Library of Munich, Germany.
    5. Kerkhof, F.L.J., 2003. "Model risk analysis for risk management and option pricing," Other publications TiSEM 01692df5-4c2d-4ed2-8108-4, Tilburg University, School of Economics and Management.
    6. Duffie, Darrell, 2003. "Intertemporal asset pricing theory," 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 11, pages 639-742, Elsevier.
    7. Santa-Clara, Pedro & Sornette, Didier, 2001. "The Dynamics of the Forward Interest Rate Curve with Stochastic String Shocks," The Review of Financial Studies, Society for Financial Studies, vol. 14(1), pages 149-185.
    8. 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.
    9. 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.
    10. Ying Jiao & Chunhua Ma & Simone Scotti, 2016. "Alpha-CIR Model with Branching Processes in Sovereign Interest Rate Modelling," Working Papers hal-01275397, HAL.
    11. Tao L. Wu & Shengqiang Xu, 2014. "A Random Field LIBOR Market Model," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 34(6), pages 580-606, June.
    12. Rama Cont & Marvin S. Mueller, 2019. "A stochastic partial differential equation model for limit order book dynamics," Papers 1904.03058, arXiv.org, revised May 2021.
    13. Zhongliang Tuo, 2013. "Hedging Against the Interest-rate Risk by Measuring the Yield-curve Movement," Papers 1312.6841, arXiv.org.
    14. Longstaff, Francis A. & Santa-Clara, Pedro & Schwartz, Eduardo S., 2001. "Throwing away a billion dollars: the cost of suboptimal exercise strategies in the swaptions market," Journal of Financial Economics, Elsevier, vol. 62(1), pages 39-66, October.
    15. Donatien Hainaut, 2018. "Calendar Spread Exchange Options Pricing with Gaussian Random Fields," Risks, MDPI, vol. 6(3), pages 1-33, August.
    16. Meifang Chu, 1997. "The Random Yield Curve and Interest Rate Options," Finance 9710003, University Library of Munich, Germany.
    17. Pierre Collin‐Dufresne & Robert S. Goldstein, 2002. "Do Bonds Span the Fixed Income Markets? Theory and Evidence for Unspanned Stochastic Volatility," Journal of Finance, American Finance Association, vol. 57(4), pages 1685-1730, August.
    18. Buraschi, Andrea & Corielli, Francesco, 2005. "Risk management implications of time-inconsistency: Model updating and recalibration of no-arbitrage models," Journal of Banking & Finance, Elsevier, vol. 29(11), pages 2883-2907, November.
    19. Kerkhof, F.L.J. & Pelsser, A., 2002. "Observational Equivalence of Discrete String Models and Market Models," Discussion Paper 2002-28, Tilburg University, Center for Economic Research.
    20. Martellosio, Federico, 2008. "Power Properties of Invariant Tests for Spatial Autocorrelation in Linear Regression," MPRA Paper 7255, University Library of Munich, Germany.

    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:hal:cesptp:hal-03018478. 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: CCSD (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    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.