IDEAS home Printed from https://ideas.repec.org/p/hal/journl/halshs-04506681.html
   My bibliography  Save this paper

The Computation of Risk Budgets under the Lévy Process Assumption

Author

Listed:
  • Olivier Le Courtois

    (EM - EMLyon Business School)

  • Christian Walter

    (LAP - Laboratoire d’anthropologie politique – Approches interdisciplinaires et critiques des mondes contemporains, UMR 8177 - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique)

Abstract

This paper revisits the computation of Value-at-Risk and other risk indicators based on the use of Lévy processes. We first provide a new presentation of Variance Gamma Processes with Drift: we reconstruct them in an original way, starting from the exponential distribution. Then, we derive general Fourier formulas that allow us to compute VaR quickly and efficiently, but also other typical indicators like Tail Conditional Expectation (TCE). Based on such a formula, we conduct a study of the term structure of VaR, and provide a discussion of the Basle 2 and Solvency II agreements

Suggested Citation

  • Olivier Le Courtois & Christian Walter, 2014. "The Computation of Risk Budgets under the Lévy Process Assumption," Post-Print halshs-04506681, HAL.
  • Handle: RePEc:hal:journl:halshs-04506681
    DOI: 10.3917/fina.352.0087
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-04506681v1
    as

    Download full text from publisher

    File URL: https://shs.hal.science/halshs-04506681v1/document
    Download Restriction: no

    File URL: https://libkey.io/10.3917/fina.352.0087?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
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. S. G. Kou, 2002. "A Jump-Diffusion Model for Option Pricing," Management Science, INFORMS, vol. 48(8), pages 1086-1101, August.
    2. Eberlein, Ernst & Keller, Ulrich & Prause, Karsten, 1998. "New Insights into Smile, Mispricing, and Value at Risk: The Hyperbolic Model," The Journal of Business, University of Chicago Press, vol. 71(3), pages 371-405, July.
    3. Thierry Ané & Hélyette Geman, 2000. "Order Flow, Transaction Clock, and Normality of Asset Returns," Journal of Finance, American Finance Association, vol. 55(5), pages 2259-2284, October.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Gian P. Cervellera & Marco P. Tucci, 2017. "A note on the Estimation of a Gamma-Variance Process: Learning from a Failure," Computational Economics, Springer;Society for Computational Economics, vol. 49(3), pages 363-385, March.
    2. Olivier Courtois, 2018. "Some Further Results on the Tempered Multistable Approach," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 25(2), pages 87-109, June.
    3. Silvia Faroni & Olivier Le Courtois & Krzysztof Ostaszewski, 2022. "Equivalent Risk Indicators: VaR, TCE, and Beyond," Risks, MDPI, vol. 10(8), pages 1-19, July.
    4. Salem, Marwa Belhaj & Fouladirad, Mitra & Deloux, Estelle, 2022. "Variance Gamma process as degradation model for prognosis and imperfect maintenance of centrifugal pumps," Reliability Engineering and System Safety, Elsevier, vol. 223(C).
    5. Bertrand Tavin & Lorenz Schneider, 2018. "From the Samuelson volatility effect to a Samuelson correlation effect : An analysis of crude oil calendar spread options," Post-Print hal-02311970, HAL.

    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. Fotopoulos, Stergios B., 2017. "Symmetric Gaussian mixture distributions with GGC scales," Journal of Multivariate Analysis, Elsevier, vol. 160(C), pages 185-194.
    2. Jose Cruz & Maria Grossinho & Daniel Sevcovic & Cyril Izuchukwu Udeani, 2022. "Linear and Nonlinear Partial Integro-Differential Equations arising from Finance," Papers 2207.11568, arXiv.org.
    3. Eckhard Platen & Hardy Hulley, 2008. "Hedging for the Long Run," Research Paper Series 214, Quantitative Finance Research Centre, University of Technology, Sydney.
    4. Carr, Peter & Wu, Liuren, 2004. "Time-changed Levy processes and option pricing," Journal of Financial Economics, Elsevier, vol. 71(1), pages 113-141, January.
    5. Denis Belomestny & Markus Reiß, 2006. "Spectral calibration of exponential Lévy models," Finance and Stochastics, Springer, vol. 10(4), pages 449-474, December.
    6. Khaled Salhi, 2017. "Pricing European options and risk measurement under exponential Lévy models — a practical guide," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 4(02n03), pages 1-36, June.
    7. Sun, Qi & Xu, Weidong, 2015. "Pricing foreign equity option with stochastic volatility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 437(C), pages 89-100.
    8. Akihiko Takahashi & Akira Yamazaki, 2008. "Efficient Static Replication of European Options under Exponential Levy Models," CIRJE F-Series CIRJE-F-539, CIRJE, Faculty of Economics, University of Tokyo.
    9. Oleg Kudryavtsev & Sergei Levendorskiǐ, 2009. "Fast and accurate pricing of barrier options under Lévy processes," Finance and Stochastics, Springer, vol. 13(4), pages 531-562, September.
    10. Lorenzo Torricelli, 2016. "Valuation of asset and volatility derivatives using decoupled time-changed Lévy processes," Review of Derivatives Research, Springer, vol. 19(1), pages 1-39, April.
    11. Mr. Noureddine Krichene, 2005. "Subordinated Levy Processes and Applications to Crude Oil Options," IMF Working Papers 2005/174, International Monetary Fund.
    12. Liming Feng & Vadim Linetsky, 2008. "Pricing Discretely Monitored Barrier Options And Defaultable Bonds In Lévy Process Models: A Fast Hilbert Transform Approach," Mathematical Finance, Wiley Blackwell, vol. 18(3), pages 337-384, July.
    13. Paweł Kliber, 2019. "Continuous and jump changes in prices processes in the selected stock markets," Collegium of Economic Analysis Annals, Warsaw School of Economics, Collegium of Economic Analysis, issue 54, pages 333-344.
    14. Christian Walter, 2020. "Sustainable Financial Risk Modelling Fitting the SDGs: Some Reflections," Sustainability, MDPI, vol. 12(18), pages 1-28, September.
    15. Bates, David S., 2012. "U.S. stock market crash risk, 1926–2010," Journal of Financial Economics, Elsevier, vol. 105(2), pages 229-259.
    16. Maurya, Vikas & Singh, Ankit & Yadav, Vivek S. & Rajpoot, Manoj K., 2024. "Efficient pricing of options in jump–diffusion models: Novel implicit–explicit methods for numerical valuation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 217(C), pages 202-225.
    17. Wendong Zheng & Chi Hung Yuen & Yue Kuen Kwok, 2016. "Recursive Algorithms For Pricing Discrete Variance Options And Volatility Swaps Under Time-Changed Lévy Processes," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(02), pages 1-29, March.
    18. David S. Bates, 2009. "U.S. Stock Market Crash Risk, 1926-2006," NBER Working Papers 14913, National Bureau of Economic Research, Inc.
    19. Peter Carr & Liuren Wu, 2014. "Static Hedging of Standard Options," Journal of Financial Econometrics, Oxford University Press, vol. 12(1), pages 3-46.
    20. Viktor Stojkoski & Trifce Sandev & Lasko Basnarkov & Ljupco Kocarev & Ralf Metzler, 2020. "Generalised geometric Brownian motion: Theory and applications to option pricing," Papers 2011.00312, 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:hal:journl:halshs-04506681. 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.