IDEAS home Printed from https://ideas.repec.org/a/eee/finlet/v6y2009i2p95-105.html
   My bibliography  Save this article

Value-at-Risk computation by Fourier inversion with explicit error bounds

Author

Listed:
  • Siven, Johannes Vitalis
  • Lins, Jeffrey Todd
  • Szymkowiak-Have, Anna

Abstract

The Value-at-Risk of a delta-gamma approximated derivatives portfolio can be computed by numerical integration of the characteristic function. However, while the choice of parameters in any numerical integration scheme is paramount, in practice it often relies on ad hoc procedures of trial and error. For normal and multivariate t-distributed risk factors, we show how to calculate the necessary parameters for one particular integration scheme as a function of the data (the distribution of risk factors, and delta and gamma) in order to satisfy a given error tolerance. This allows for implementation in a fully automated risk management system. We also demonstrate in simulations that the method is significantly faster than the Monte Carlo method, for a given error tolerance.

Suggested Citation

  • Siven, Johannes Vitalis & Lins, Jeffrey Todd & Szymkowiak-Have, Anna, 2009. "Value-at-Risk computation by Fourier inversion with explicit error bounds," Finance Research Letters, Elsevier, vol. 6(2), pages 95-105, June.
    • Handle: RePEc:eee:finlet:v:6:y:2009:i:2:p:95-105
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S1544-6123(08)00065-2
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. Jun Pan & Darrell Duffie, 2001. "Analytical value-at-risk with jumps and credit risk," Finance and Stochastics, Springer, vol. 5(2), pages 155-180.
    2. Paul Glasserman & Philip Heidelberger & Perwez Shahabuddin, 2002. "Portfolio Value‐at‐Risk with Heavy‐Tailed Risk Factors," Mathematical Finance, Wiley Blackwell, vol. 12(3), pages 239-269, July.
    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. Mitra, Sovan, 2017. "Efficient option risk measurement with reduced model risk," Insurance: Mathematics and Economics, Elsevier, vol. 72(C), pages 163-174.
    2. Ruili Sun & Tiefeng Ma & Shuangzhe Liu & Milind Sathye, 2019. "Improved Covariance Matrix Estimation for Portfolio Risk Measurement: A Review," JRFM, MDPI, vol. 12(1), pages 1-34, March.
    3. Alex YiHou Huang, 2010. "An optimization process in Value‐at‐Risk estimation," Review of Financial Economics, John Wiley & Sons, vol. 19(3), pages 109-116, August.
    4. Leitao, Álvaro & Oosterlee, Cornelis W. & Ortiz-Gracia, Luis & Bohte, Sander M., 2018. "On the data-driven COS method," Applied Mathematics and Computation, Elsevier, vol. 317(C), pages 68-84.

    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. Sadefo Kamdem, J. & Genz, A., 2008. "Approximation of multiple integrals over hyperboloids with application to a quadratic portfolio with options," Computational Statistics & Data Analysis, Elsevier, vol. 52(7), pages 3389-3407, March.
    2. Grundke, Peter, 2009. "Importance sampling for integrated market and credit portfolio models," European Journal of Operational Research, Elsevier, vol. 194(1), pages 206-226, April.
    3. Seyed Mohammad Sina Seyfi & Azin Sharifi & Hamidreza Arian, 2020. "Portfolio Risk Measurement Using a Mixture Simulation Approach," Papers 2011.07994, arXiv.org.
    4. Bardou O. & Frikha N. & Pagès G., 2009. "Computing VaR and CVaR using stochastic approximation and adaptive unconstrained importance sampling," Monte Carlo Methods and Applications, De Gruyter, vol. 15(3), pages 173-210, January.
    5. Olivier Aj Bardou & Noufel Frikha & G. Pag`es, 2008. "Computation of VaR and CVaR using stochastic approximations and unconstrained importance sampling," Papers 0812.3381, arXiv.org, revised Dec 2010.
    6. Seyfi, Seyed Mohammad Sina & Sharifi, Azin & Arian, Hamidreza, 2021. "Portfolio Value-at-Risk and expected-shortfall using an efficient simulation approach based on Gaussian Mixture Model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 1056-1079.
    7. Torben G. Andersen & Tim Bollerslev & Peter Christoffersen & Francis X. Diebold, 2007. "Practical Volatility and Correlation Modeling for Financial Market Risk Management," NBER Chapters, in: The Risks of Financial Institutions, pages 513-544, National Bureau of Economic Research, Inc.
    8. Raymond BRUMMELHUIS & Jules Sadefo-Kamdem, 2009. "Var For Quadratic Portfolio'S With Generalized Laplace Distributed Returns," Working Papers 09-06, LAMETA, Universtiy of Montpellier, revised Jun 2009.
    9. Christensen, Kim & Oomen, Roel C.A. & Podolskij, Mark, 2014. "Fact or friction: Jumps at ultra high frequency," Journal of Financial Economics, Elsevier, vol. 114(3), pages 576-599.
    10. Pierre Nyquist, 2013. "Moderate deviations for importance sampling estimators of risk measures," Papers 1306.6588, arXiv.org.
    11. Breuer, Thomas & Jandacka, Martin & Rheinberger, Klaus & Summer, Martin, 2010. "Does adding up of economic capital for market- and credit risk amount to conservative risk assessment?," Journal of Banking & Finance, Elsevier, vol. 34(4), pages 703-712, April.
    12. Mark Broadie & Yiping Du & Ciamac C. Moallemi, 2015. "Risk Estimation via Regression," Operations Research, INFORMS, vol. 63(5), pages 1077-1097, October.
    13. J. Christopher Westland, 2015. "Economics of eBay’s buyer protection plan," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 1(1), pages 1-20, December.
    14. Mbairadjim Moussa, A. & Sadefo Kamdem, J. & Terraza, M., 2014. "Fuzzy value-at-risk and expected shortfall for portfolios with heavy-tailed returns," Economic Modelling, Elsevier, vol. 39(C), pages 247-256.
    15. Leung, Melvern & Li, Youwei & Pantelous, Athanasios A. & Vigne, Samuel A., 2021. "Bayesian Value-at-Risk backtesting: The case of annuity pricing," European Journal of Operational Research, Elsevier, vol. 293(2), pages 786-801.
    16. Lu, Zhaoyang, 2011. "Modeling the yearly Value-at-Risk for operational risk in Chinese commercial banks," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(4), pages 604-616.
    17. Shih-Kuei Lin & Ren-Her Wang & Cheng-Der Fuh, 2006. "Risk Management for Linear and Non-Linear Assets: A Bootstrap Method with Importance Resampling to Evaluate Value-at-Risk," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 13(3), pages 261-295, September.
    18. Lin, Shih-Kuei & Wang, Shin-Yun & Chen, Carl R. & Xu, Lian-Wen, 2017. "Pricing Range Accrual Interest Rate Swap employing LIBOR market models with jump risks," The North American Journal of Economics and Finance, Elsevier, vol. 42(C), pages 359-373.
    19. Liao, Yin, 2013. "The benefit of modeling jumps in realized volatility for risk prediction: Evidence from Chinese mainland stocks," Pacific-Basin Finance Journal, Elsevier, vol. 23(C), pages 25-48.
    20. repec:wyi:journl:002108 is not listed on IDEAS
    21. Su, Zhifang & Bao, Haohua & Li, Qifang & Xu, Boyu & Cui, Xin, 2022. "The prediction of price gap anomaly in Chinese stock market: Evidence from the dependent functional logit model," Finance Research Letters, Elsevier, vol. 47(PB).

    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:finlet:v:6:y:2009:i:2:p:95-105. 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/locate/frl .

    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.