IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v130y2020i6p3753-3801.html
   My bibliography  Save this article

Analysis of a micro–macro acceleration method with minimum relative entropy moment matching

Author

Listed:
  • Lelièvre, Tony
  • Samaey, Giovanni
  • Zieliński, Przemysław

Abstract

We analyse convergence of a micro–macro acceleration method for the simulation of stochastic differential equations with time-scale separation. The method alternates short bursts of path simulations with the extrapolation of macroscopic state variables forward in time. After extrapolation, a new microscopic state is constructed, consistent with the extrapolated macroscopic state, that minimises the perturbation caused by the extrapolation in a relative entropy sense. We study local errors and numerical stability of the method to prove its convergence to the full microscopic dynamics when the extrapolation time step tends to zero and the number of macroscopic state variables tends to infinity.

Suggested Citation

  • Lelièvre, Tony & Samaey, Giovanni & Zieliński, Przemysław, 2020. "Analysis of a micro–macro acceleration method with minimum relative entropy moment matching," Stochastic Processes and their Applications, Elsevier, vol. 130(6), pages 3753-3801.
    • Handle: RePEc:eee:spapps:v:130:y:2020:i:6:p:3753-3801
    DOI: 10.1016/j.spa.2019.10.008
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414919306039
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2019.10.008?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Marco Avellaneda, 1998. "Minimum-Relative-Entropy Calibration of Asset-Pricing Models," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 1(04), pages 447-472.
    2. Marco Avellaneda & Craig Friedman & Richard Holmes & Dominick Samperi, 1997. "Calibrating volatility surfaces via relative-entropy minimization," Applied Mathematical Finance, Taylor & Francis Journals, vol. 4(1), pages 37-64.
    3. Ilg, Patrick & Karlin, Iliya V. & Öttinger, Hans Christian, 2002. "Canonical distribution functions in polymer dynamics. (I). Dilute solutions of flexible polymers," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 315(3), pages 367-385.
    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. Vladislav Kargin, 2003. "Consistent Estimation of Pricing Kernels from Noisy Price Data," Papers math/0310223, arXiv.org.
    2. Vinicius Albani & Adriano De Cezaro & Jorge P. Zubelli, 2017. "Convex Regularization Of Local Volatility Estimation," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(01), pages 1-37, February.
    3. A. Monteiro & R. Tütüncü & L. Vicente, 2011. "Estimation of risk-neutral density surfaces," Computational Management Science, Springer, vol. 8(4), pages 387-414, November.
    4. Carr, Peter & Geman, Helyette & Madan, Dilip B., 2001. "Pricing and hedging in incomplete markets," Journal of Financial Economics, Elsevier, vol. 62(1), pages 131-167, October.
    5. Jiangze Du & Shaojie Lai & Kin Keung Lai & Shifei Zhou, 2021. "A novel term structure stochastic model with adaptive correlation for trend analysis," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 26(4), pages 5485-5498, October.
    6. Tapiero, Oren J., 2013. "A maximum (non-extensive) entropy approach to equity options bid–ask spread," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(14), pages 3051-3060.
    7. Fard, Farzad Alavi & Siu, Tak Kuen, 2013. "Pricing participating products with Markov-modulated jump–diffusion process: An efficient numerical PIDE approach," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 712-721.
    8. Ilg, Patrick, 2008. "Macroscopic thermodynamics of flowing polymers derived from systematic coarse-graining procedure," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(26), pages 6484-6496.
    9. Thomas Breuer & Martin Summer, 2013. "Stress Test Robustness: Recent Advances and Open Problems," Financial Stability Report, Oesterreichische Nationalbank (Austrian Central Bank), issue 25, pages 74-86.
    10. Ivan Guo & Gregoire Loeper & Jan Obloj & Shiyi Wang, 2021. "Optimal transport for model calibration," Papers 2107.01978, arXiv.org.
    11. Ivan Guo & Gregoire Loeper, 2018. "Path Dependent Optimal Transport and Model Calibration on Exotic Derivatives," Papers 1812.03526, arXiv.org, revised Sep 2020.
    12. Sebastian Jaimungal & Silvana M. Pesenti & Leandro S'anchez-Betancourt, 2022. "Minimal Kullback-Leibler Divergence for Constrained L\'evy-It\^o Processes," Papers 2206.14844, arXiv.org, revised Aug 2022.
    13. Alexander Veremyev & Peter Tsyurmasto & Stan Uryasev & R. Rockafellar, 2014. "Calibrating probability distributions with convex-concave-convex functions: application to CDO pricing," Computational Management Science, Springer, vol. 11(4), pages 341-364, October.
    14. Ilia Bouchouev & Victor Isakov & Nicolas Valdivia, 2002. "Recovery of volatility coefficient by linearization," Quantitative Finance, Taylor & Francis Journals, vol. 2(4), pages 257-263.
    15. Paul Glasserman & Bin Yu, 2005. "Large Sample Properties of Weighted Monte Carlo Estimators," Operations Research, INFORMS, vol. 53(2), pages 298-312, April.
    16. Breuer, Thomas & Csiszár, Imre, 2013. "Systematic stress tests with entropic plausibility constraints," Journal of Banking & Finance, Elsevier, vol. 37(5), pages 1552-1559.
    17. Cristian Homescu, 2011. "Implied Volatility Surface: Construction Methodologies and Characteristics," Papers 1107.1834, arXiv.org.
    18. Rienäcker, G. & Kröger, M. & Hess, S., 2002. "Chaotic and regular shear-induced orientational dynamics of nematic liquid crystals," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 315(3), pages 537-568.
    19. José L. Vilar-Zanón & Olivia Peraita-Ezcurra, 2019. "A linear goal programming method to recover risk neutral probabilities from options prices by maximum entropy," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 42(1), pages 259-276, June.
    20. Lishang Jiang & Qihong Chen & Lijun Wang & Jin Zhang, 2003. "A new well-posed algorithm to recover implied local volatility," Quantitative Finance, Taylor & Francis Journals, vol. 3(6), pages 451-457.

    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:eee:spapps:v:130:y:2020:i:6:p:3753-3801. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description .

    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.