IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v176y2010i1p293-30910.1007-s10479-008-0468-1.html
   My bibliography  Save this article

Stochastic models for risk estimation in volatile markets: a survey

Author

Listed:
  • Stoyan Stoyanov
  • Borjana Racheva-Iotova
  • Svetlozar Rachev
  • Frank Fabozzi

Abstract

Portfolio risk estimation in volatile markets requires employing fat-tailed models for financial returns combined with copula functions to capture asymmetries in dependence and an appropriate downside risk measure. In this survey, we discuss how these three essential components can be combined together in a Monte Carlo based framework for risk estimation and risk capital allocation with the average value-at-risk measure (AVaR). AVaR is the average loss provided that the loss is larger than a predefined value-at-risk level. We consider in some detail the AVaR calculation and estimation and investigate the stochastic stability. Copyright Springer Science+Business Media, LLC 2010

Suggested Citation

  • Stoyan Stoyanov & Borjana Racheva-Iotova & Svetlozar Rachev & Frank Fabozzi, 2010. "Stochastic models for risk estimation in volatile markets: a survey," Annals of Operations Research, Springer, vol. 176(1), pages 293-309, April.
    • Handle: RePEc:spr:annopr:v:176:y:2010:i:1:p:293-309:10.1007/s10479-008-0468-1
    DOI: 10.1007/s10479-008-0468-1
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10479-008-0468-1
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10479-008-0468-1?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. Aleksander Janicki & Aleksander Weron, 1994. "Simulation and Chaotic Behavior of Alpha-stable Stochastic Processes," HSC Books, Hugo Steinhaus Center, Wroclaw University of Technology, number hsbook9401.
    2. Eckhard Platen & Renata Rendek, 2007. "Empirical Evidence on Student-t Log-Returns of Diversified World Stock Indices," Research Paper Series 194, Quantitative Finance Research Centre, University of Technology, Sydney.
    3. Kim, Young Shin & Rachev, Svetlozar T. & Bianchi, Michele Leonardo & Fabozzi, Frank J., 2008. "Financial market models with Lévy processes and time-varying volatility," Journal of Banking & Finance, Elsevier, vol. 32(7), pages 1363-1378, July.
    4. Simon Hurst & Eckhard Platen & Svetlozar Rachev, 1997. "Subordinated Market Index Models: A Comparison," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 4(2), pages 97-124, May.
    5. Benoit Mandelbrot, 2015. "The Variation of Certain Speculative Prices," World Scientific Book Chapters, in: Anastasios G Malliaris & William T Ziemba (ed.), THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78, World Scientific Publishing Co. Pte. Ltd..
    6. Eugene F. Fama, 1963. "Mandelbrot and the Stable Paretian Hypothesis," The Journal of Business, University of Chicago Press, vol. 36, pages 420-420.
    7. Rockafellar, R. Tyrrell & Uryasev, Stanislav, 2002. "Conditional value-at-risk for general loss distributions," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1443-1471, July.
    8. Sun Wei & Rachev Svetlozar & Stoyanov Stoyan V. & Fabozzi Frank J., 2008. "Multivariate Skewed Student's t Copula in the Analysis of Nonlinear and Asymmetric Dependence in the German Equity Market," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 12(2), pages 1-37, May.
    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. Kenichiro Shiraya & Tomohisa Yamakami, 2023. "Constructing Copulas Using Corrected Hermite Polynomial Expansion for Estimating Cross Foreign Exchange Volatility," Papers 2301.10044, arXiv.org.
    2. Vladik Kreinovich & Monchaya Chiangpradit & Wararit Panichkitkosolkul, 2012. "Efficient algorithms for heavy-tail analysis under interval uncertainty," Annals of Operations Research, Springer, vol. 195(1), pages 73-96, May.
    3. Vincenzo Pacelli & Francesca Pampurini & Anna Grazia Quaranta, 2023. "Environmental, Social and Governance investing: Does rating matter?," Business Strategy and the Environment, Wiley Blackwell, vol. 32(1), pages 30-41, January.
    4. Yinping You & Xiaohu Li, 2017. "Most unfavorable deductibles and coverage limits for multiple random risks with Archimedean copulas," Annals of Operations Research, Springer, vol. 259(1), pages 485-501, December.
    5. Darinka Dentcheva & Spiridon Penev & Andrzej Ruszczyński, 2017. "Statistical estimation of composite risk functionals and risk optimization problems," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(4), pages 737-760, August.
    6. Fulga, Cristinca, 2016. "Portfolio optimization under loss aversion," European Journal of Operational Research, Elsevier, vol. 251(1), pages 310-322.
    7. Young Shin Kim, 2022. "Portfolio optimization and marginal contribution to risk on multivariate normal tempered stable model," Annals of Operations Research, Springer, vol. 312(2), pages 853-881, May.
    8. Michele Leonardo Bianchi & Gian Luca Tassinari, 2018. "Forward-looking portfolio selection with multivariate non-Gaussian models and the Esscher transform," Papers 1805.05584, arXiv.org, revised May 2018.
    9. Johan Dahlin & Mattias Villani & Thomas B. Schon, 2015. "Bayesian optimisation for fast approximate inference in state-space models with intractable likelihoods," Papers 1506.06975, arXiv.org, revised Jun 2017.
    10. Haijun Li & Susan Xu & Way Kuo, 2014. "Asymptotic analysis of simultaneous damages in spatial Boolean models," Annals of Operations Research, Springer, vol. 212(1), pages 139-154, January.
    11. Xun Lu & Kin Lai & Liang Liang, 2014. "Portfolio value-at-risk estimation in energy futures markets with time-varying copula-GARCH model," Annals of Operations Research, Springer, vol. 219(1), pages 333-357, August.
    12. Jianxu Liu & Quanrui Song & Yang Qi & Sanzidur Rahman & Songsak Sriboonchitta, 2020. "Measurement of Systemic Risk in Global Financial Markets and Its Application in Forecasting Trading Decisions," Sustainability, MDPI, vol. 12(10), pages 1-15, May.
    13. Stoyan Stoyanov & Svetlozar Rachev & Frank Fabozzi, 2013. "Sensitivity of portfolio VaR and CVaR to portfolio return characteristics," Annals of Operations Research, Springer, vol. 205(1), pages 169-187, May.
    14. Wu, Xu & Zhang, Linlin & Li, Jia & Yan, Ruzhen, 2021. "Fractal statistical measure and portfolio model optimization under power-law distribution," The North American Journal of Economics and Finance, Elsevier, vol. 58(C).

    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. Fabozzi Frank J. & Stoyanov Stoyan V. & Rachev Svetlozar T., 2013. "Computational aspects of portfolio risk estimation in volatile markets: a survey," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 17(1), pages 103-120, February.
    2. Detlef Seese & Christof Weinhardt & Frank Schlottmann (ed.), 2008. "Handbook on Information Technology in Finance," International Handbooks on Information Systems, Springer, number 978-3-540-49487-4, November.
    3. Mercik, Szymon & Weron, Rafal, 2002. "Origins of scaling in FX markets," MPRA Paper 2294, University Library of Munich, Germany.
    4. Young Kim & Rosella Giacometti & Svetlozar Rachev & Frank Fabozzi & Domenico Mignacca, 2012. "Measuring financial risk and portfolio optimization with a non-Gaussian multivariate model," Annals of Operations Research, Springer, vol. 201(1), pages 325-343, December.
    5. Rachev, Svetlozar & Jasic, Teo & Stoyanov, Stoyan & Fabozzi, Frank J., 2007. "Momentum strategies based on reward-risk stock selection criteria," Journal of Banking & Finance, Elsevier, vol. 31(8), pages 2325-2346, August.
    6. Jovanovic, Franck & Schinckus, Christophe, 2017. "Econophysics and Financial Economics: An Emerging Dialogue," OUP Catalogue, Oxford University Press, number 9780190205034, Decembrie.
    7. Kevin John Fergusson, 2018. "Less-Expensive Pricing and Hedging of Extreme-Maturity Interest Rate Derivatives and Equity Index Options Under the Real-World Measure," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 3-2018.
    8. Shao, Barret Pengyuan & Rachev, Svetlozar T. & Mu, Yu, 2015. "Applied mean-ETL optimization in using earnings forecasts," International Journal of Forecasting, Elsevier, vol. 31(2), pages 561-567.
    9. Abhinav Anand & Tiantian Li & Tetsuo Kurosaki & Young Shin Kim, 2017. "The equity risk posed by the too-big-to-fail banks: a Foster–Hart estimation," Annals of Operations Research, Springer, vol. 253(1), pages 21-41, June.
    10. Ortobelli, Sergio & Rachev, Svetlozar & Schwartz, Eduardo, 2000. "The Problem of Optimal Asset Allocation with Stable Distributed Returns," University of California at Los Angeles, Anderson Graduate School of Management qt3zd6q86c, Anderson Graduate School of Management, UCLA.
    11. Yoshio Miyahara & Alexander Novikov, 2001. "Geometric Lévy Process Pricing Model," Research Paper Series 66, Quantitative Finance Research Centre, University of Technology, Sydney.
    12. Robert Elliott & Hong Miao, 2009. "VaR and expected shortfall: a non-normal regime switching framework," Quantitative Finance, Taylor & Francis Journals, vol. 9(6), pages 747-755.
    13. López Martín, María del Mar & García, Catalina García & García Pérez, José, 2012. "Treatment of kurtosis in financial markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(5), pages 2032-2045.
    14. Young Shin Kim, 2022. "Portfolio optimization and marginal contribution to risk on multivariate normal tempered stable model," Annals of Operations Research, Springer, vol. 312(2), pages 853-881, May.
    15. K. Fergusson, 2017. "Explicit Formulae For Parameters Of Stochastic Models Of A Discounted Equity Index Using Maximum Likelihood Estimation With Applications," Annals of Financial Economics (AFE), World Scientific Publishing Co. Pte. Ltd., vol. 12(02), pages 1-31, June.
    16. Steven Kou, 2000. "A Jump Diffusion Model for Option Pricing with Three Properties: Leptokurtic Feature, Volatility Smile, and Analytical Tractability," Econometric Society World Congress 2000 Contributed Papers 0062, Econometric Society.
    17. Young Shin Kim, 2020. "Portfolio Optimization on the Dispersion Risk and the Asymmetric Tail Risk," Papers 2007.13972, arXiv.org, revised Sep 2020.
    18. De Giovanni, Domenico & Ortobelli, Sergio & Rachev, Svetlozar, 2008. "Delta hedging strategies comparison," European Journal of Operational Research, Elsevier, vol. 185(3), pages 1615-1631, March.
    19. Dominique Guégan & Wayne Tarrant, 2012. "On the necessity of five risk measures," Annals of Finance, Springer, vol. 8(4), pages 533-552, November.
    20. Lombardi, Marco J. & Calzolari, Giorgio, 2009. "Indirect estimation of [alpha]-stable stochastic volatility models," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2298-2308, April.

    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:spr:annopr:v:176:y:2010:i:1:p:293-309:10.1007/s10479-008-0468-1. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.