IDEAS home Printed from https://ideas.repec.org/p/cam/camdae/0506.html
   My bibliography  Save this paper

Copula Based Monte Carlo Integration in Financial Problems

Author

Listed:
  • Sancetta, A.

Abstract

A computational technique that transform integrals over RK, or some of its subsets, into the hypercube [0, 1]K can be exploited in order to solve integrals via Monte Carlo integration without the need to simulate from the original distribution; all that is needed is to simulate iid uniform [0, 1] pseudo random variables. In particular the technique arises from the copula representation of multivariate distributions and the use of the marginal quantile function of the data. The procedure is further simplified if the quantile function has closed form. Several financial applications are considered in order to highlight the scope of this numerical technique for financial problems

Suggested Citation

  • Sancetta, A., 2005. "Copula Based Monte Carlo Integration in Financial Problems," Cambridge Working Papers in Economics 0506, Faculty of Economics, University of Cambridge.
    • Handle: RePEc:cam:camdae:0506
    Note: EM
    as

    Download full text from publisher

    File URL: https://files.econ.cam.ac.uk/repec/cam/pdf/cwpe0506.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. P. Silvapulle & C. W. J. Granger, 2001. "Large returns, conditional correlation and portfolio diversification: a value-at-risk approach," Quantitative Finance, Taylor & Francis Journals, vol. 1(5), pages 542-551.
    2. Rimas Norvaisa, 2000. "Modelling of stock price changes: A real analysis approach," Finance and Stochastics, Springer, vol. 4(3), pages 343-369.
    3. David E. Bell & Peter C. Fishburn, 2001. "Strong One-Switch Utility," Management Science, INFORMS, vol. 47(4), pages 601-604, April.
    4. Geweke, John, 1996. "Monte carlo simulation and numerical integration," Handbook of Computational Economics, in: H. M. Amman & D. A. Kendrick & J. Rust (ed.), Handbook of Computational Economics, edition 1, volume 1, chapter 15, pages 731-800, Elsevier.
    5. Li, Haijun & Scarsini, Marco & Shaked, Moshe, 1996. "Linkages: A Tool for the Construction of Multivariate Distributions with Given Nonoverlapping Multivariate Marginals," Journal of Multivariate Analysis, Elsevier, vol. 56(1), pages 20-41, January.
    6. David E. Bell, 1988. "One-Switch Utility Functions and a Measure of Risk," Management Science, INFORMS, vol. 34(12), pages 1416-1424, December.
    7. J. V. Andersen & D. Sornette, 1999. "Have your cake and eat it too: increasing returns while lowering large risks!," Papers cond-mat/9907217, arXiv.org.
    8. A. Sancetta & Satchell, S.E., 2001. "Bernstein Approximations to the Copula Function and Portfolio Optimization," Cambridge Working Papers in Economics 0105, Faculty of Economics, University of Cambridge.
    9. Ding, Zhuanxin & Granger, Clive W. J. & Engle, Robert F., 1993. "A long memory property of stock market returns and a new model," Journal of Empirical Finance, Elsevier, vol. 1(1), pages 83-106, June.
    10. Jackwerth, Jens Carsten, 2000. "Recovering Risk Aversion from Option Prices and Realized Returns," The Review of Financial Studies, Society for Financial Studies, vol. 13(2), pages 433-451.
    11. Ines Fortin & Christoph Kuzmics, 2002. "Tail‐dependence in stock‐return pairs," Intelligent Systems in Accounting, Finance and Management, John Wiley & Sons, Ltd., vol. 11(2), pages 89-107, April.
    12. Scarsini, Marco, 1989. "Copulae of probability measures on product spaces," Journal of Multivariate Analysis, Elsevier, vol. 31(2), pages 201-219, November.
    13. François Longin & Bruno Solnik, 2001. "Extreme Correlation of International Equity Markets," Journal of Finance, American Finance Association, vol. 56(2), pages 649-676, April.
    14. Mandelbrot, Benoit B, 1972. "Correction of an Error in "The Variation of Certain Speculative Prices" (1963)," The Journal of Business, University of Chicago Press, vol. 45(4), pages 542-543, October.
    15. J. L. Knight & S. E. Satchell & K. C. Tran, 1995. "Statistical modelling of asymmetric risk in asset returns," Applied Mathematical Finance, Taylor & Francis Journals, vol. 2(3), pages 155-172.
    16. 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..
    17. David E. Bell, 1995. "Risk, Return, and Utility," Management Science, INFORMS, vol. 41(1), pages 23-30, January.
    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. Chabi-Yo, Fousseni & Ruenzi, Stefan & Weigert, Florian, 2018. "Crash Sensitivity and the Cross Section of Expected Stock Returns," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 53(3), pages 1059-1100, June.
    2. Ghysels, E. & Harvey, A. & Renault, E., 1995. "Stochastic Volatility," Papers 95.400, Toulouse - GREMAQ.
    3. Jonathan B. Hill, 2004. "Gaussian Tests of "Extremal White Noise" for Dependent, Heterogeneous, Heavy Tailed Time Series with an Application," Econometrics 0411014, University Library of Munich, Germany, revised 04 Nov 2005.
    4. Geluk, J.L. & De Vries, C.G., 2006. "Weighted sums of subexponential random variables and asymptotic dependence between returns on reinsurance equities," Insurance: Mathematics and Economics, Elsevier, vol. 38(1), pages 39-56, February.
    5. Marco Rocco, 2011. "Extreme value theory for finance: a survey," Questioni di Economia e Finanza (Occasional Papers) 99, Bank of Italy, Economic Research and International Relations Area.
    6. Yu Wang & Haicheng Shu, 2019. "Evaluating the Performance of Factor Pricing Models for Different Stock Market Trends: Evidence from China," Working Papers 2019-10-10, Wang Yanan Institute for Studies in Economics (WISE), Xiamen University.
    7. E. Samanidou & E. Zschischang & D. Stauffer & T. Lux, 2001. "Microscopic Models of Financial Markets," Papers cond-mat/0110354, arXiv.org.
    8. Agbeyegbe, Terence D., 2015. "An inverted U-shaped crude oil price return-implied volatility relationship," Review of Financial Economics, Elsevier, vol. 27(C), pages 28-45.
    9. Loredana Ureche-Rangau & Quiterie de Rorthays, 2009. "More on the volatility-trading volume relationship in emerging markets: The Chinese stock market," Journal of Applied Statistics, Taylor & Francis Journals, vol. 36(7), pages 779-799.
    10. Booth, G. Geoffrey & Gurun, Umit G., 2008. "Volatility clustering and the bid-ask spread: Exchange rate behavior in early Renaissance Florence," Journal of Empirical Finance, Elsevier, vol. 15(1), pages 131-144, January.
    11. Koch, Nicolas, 2014. "Tail events: A new approach to understanding extreme energy commodity prices," Energy Economics, Elsevier, vol. 43(C), pages 195-205.
    12. Aleksejus Kononovicius & Julius Ruseckas, 2014. "Nonlinear GARCH model and 1/f noise," Papers 1412.6244, arXiv.org, revised Feb 2015.
    13. Teräsvirta, Timo, 2006. "An introduction to univariate GARCH models," SSE/EFI Working Paper Series in Economics and Finance 646, Stockholm School of Economics.
    14. Danilo Delpini & Giacomo Bormetti, 2012. "Stochastic Volatility with Heterogeneous Time Scales," Papers 1206.0026, arXiv.org, revised Apr 2013.
    15. Xue-Zhong He & Youwei Li, 2017. "The adaptiveness in stock markets: testing the stylized facts in the DAX 30," Journal of Evolutionary Economics, Springer, vol. 27(5), pages 1071-1094, November.
    16. Koliai, Lyes, 2016. "Extreme risk modeling: An EVT–pair-copulas approach for financial stress tests," Journal of Banking & Finance, Elsevier, vol. 70(C), pages 1-22.
    17. Trino-Manuel Ñíguez, 2008. "Volatility and VaR forecasting in the Madrid Stock Exchange," Spanish Economic Review, Springer;Spanish Economic Association, vol. 10(3), pages 169-196, September.
    18. DiTraglia, Francis J. & Gerlach, Jeffrey R., 2013. "Portfolio selection: An extreme value approach," Journal of Banking & Finance, Elsevier, vol. 37(2), pages 305-323.
    19. Electra V. Petracou & Anastasios Xepapadeas & Athanasios N. Yannacopoulos, 2022. "Decision Making Under Model Uncertainty: Fréchet–Wasserstein Mean Preferences," Management Science, INFORMS, vol. 68(2), pages 1195-1211, February.
    20. Debabrata Mukhopadhyay & Nityananda Sarkar, 2013. "Stock Returns Under Alternative Volatility and Distributional Assumptions: The Case for India," International Econometric Review (IER), Econometric Research Association, vol. 5(1), pages 1-19, April.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:cam:camdae:0506. 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: Jake Dyer (email available below). General contact details of provider: https://www.econ.cam.ac.uk/ .

    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.