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Value-at-risk Trade-off and Capital Allocation with Copulas

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  • Umberto Cherubini
  • Elisa Luciano

Abstract

type="main" xml:lang="en"> This paper uses copula functions to evaluate tail probabilities and market risk trade-offs at a given confidence level, dropping the joint normality assumption on returns. Copulas enable one to represent distribution functions separating the marginal distributions from the association structure. We present an application to two stock market indices: for each market we recover the marginal probability distribution. We then calibrate copula functions and recover the joint distribution. The estimated copulas directly give the joint probabilities of extreme losses. Their level curves measure the trade-off between losses over different desks. This trade-off can be exploited for capital allocation and is shown to depend on fat tails. (J.E.L.: C14, G19, G29).

Suggested Citation

  • Umberto Cherubini & Elisa Luciano, 2001. "Value-at-risk Trade-off and Capital Allocation with Copulas," Economic Notes, Banca Monte dei Paschi di Siena SpA, vol. 30(2), pages 235-256, July.
    • Handle: RePEc:bla:ecnote:v:30:y:2001:i:2:p:235-256
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    File URL: http://hdl.handle.net/10.1111/j.0391-5026.2001.00055.x
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    Cited by:

    1. Sergio Rey, 2014. "Fast algorithms for a space-time concordance measure," Computational Statistics, Springer, vol. 29(3), pages 799-811, June.
    2. Talbi, Marwa & Bedoui, Rihab & de Peretti, Christian & Belkacem, Lotfi, 2021. "Is the role of precious metals as precious as they are? A vine copula and BiVaR approaches," Resources Policy, Elsevier, vol. 73(C).
    3. Yanqin Fan & Xiaohong Chen & Andrew Patton, 2004. "(IAM Series No 003) Simple Tests for Models of Dependence Between Multiple Financial Time Series, with Applications to U.S. Equity Returns and Exchange Rates," FMG Discussion Papers dp483, Financial Markets Group.
    4. Leitao, Álvaro & Grzelak, Lech A. & Oosterlee, Cornelis W., 2017. "On a one time-step Monte Carlo simulation approach of the SABR model: Application to European options," Applied Mathematics and Computation, Elsevier, vol. 293(C), pages 461-479.
    5. Morettin Pedro A. & Toloi Clelia M.C. & Chiann Chang & de Miranda José C.S., 2011. "Wavelet Estimation of Copulas for Time Series," Journal of Time Series Econometrics, De Gruyter, vol. 3(3), pages 1-31, October.
    6. Garcia-Jorcano, Laura & Benito, Sonia, 2020. "Studying the properties of the Bitcoin as a diversifying and hedging asset through a copula analysis: Constant and time-varying," Research in International Business and Finance, Elsevier, vol. 54(C).
    7. Azam, Kazim & Pitt, Michael, 2014. "Bayesian Inference for a Semi-Parametric Copula-based Markov Chain," Economic Research Papers 270232, University of Warwick - Department of Economics.
    8. Escribano, Ana & Koczar, Monika W. & Jareño, Francisco & Esparcia, Carlos, 2023. "Shock transmission between crude oil prices and stock markets," Resources Policy, Elsevier, vol. 83(C).
    9. Zhou, Xinmiao & Qian, Huanhuan & Pérez-Rodríguez, Jorge. V. & González López-Valcárcel, Beatriz, 2020. "Risk dependence and cointegration between pharmaceutical stock markets: The case of China and the USA," The North American Journal of Economics and Finance, Elsevier, vol. 52(C).
    10. Alqahtani, Abdullah & Klein, Tony & Khalid, Ali, 2019. "The impact of oil price uncertainty on GCC stock markets," Resources Policy, Elsevier, vol. 64(C).
    11. Chebbi, Ali & Hedhli, Amel, 2022. "Revisiting the accuracy of standard VaR methods for risk assessment: Using the Copula–EVT multidimensional approach for stock markets in the MENA region," The Quarterly Review of Economics and Finance, Elsevier, vol. 84(C), pages 430-445.
    12. Mawuli Segnon & Mark Trede, 2018. "Forecasting market risk of portfolios: copula-Markov switching multifractal approach," The European Journal of Finance, Taylor & Francis Journals, vol. 24(14), pages 1123-1143, September.
    13. Chuan-Hsiang Han & Kun Wang, 2022. "Stressed portfolio optimization with semiparametric method," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 8(1), pages 1-34, December.
    14. Azam, Kazim & Pitt, Michael, 2014. "Bayesian Inference for a Semi-Parametric Copula-based Markov Chain," The Warwick Economics Research Paper Series (TWERPS) 1051, University of Warwick, Department of Economics.
    15. Azam, Kazim, 2014. "Dependence Analysis between Foreign Exchange Rates: A Semi-Parametric Copula Approach," Economic Research Papers 270231, University of Warwick - Department of Economics.
    16. Marius Galabe Sampid & Haslifah M Hasim & Hongsheng Dai, 2018. "Refining value-at-risk estimates using a Bayesian Markov-switching GJR-GARCH copula-EVT model," PLOS ONE, Public Library of Science, vol. 13(6), pages 1-33, June.
    17. Azam, Kazim, 2014. "Dependence Analysis between Foreign Exchange Rates: A Semi-Parametric Copula Approach," The Warwick Economics Research Paper Series (TWERPS) 1052, University of Warwick, Department of Economics.
    18. Pérez-Rodríguez, Jorge V. & Ledesma-Rodríguez, Francisco & Santana-Gallego, María, 2015. "Testing dependence between GDP and tourism's growth rates," Tourism Management, Elsevier, vol. 48(C), pages 268-282.
    19. Jorge V. Pérez-Rodríguez, 2020. "Another look at the implied and realised volatility relation: a copula-based approach," Risk Management, Palgrave Macmillan, vol. 22(1), pages 38-64, March.
    20. Patton, Andrew, 2013. "Copula Methods for Forecasting Multivariate Time Series," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 2, chapter 0, pages 899-960, Elsevier.

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