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A copula-based model of speculative price dynamics in discrete time

Author

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  • Cherubini, Umberto
  • Mulinacci, Sabrina
  • Romagnoli, Silvia

Abstract

This paper suggests a new technique to construct first order Markov processes using products of copula functions, in the spirit of Darsow et al. (1992) [10]. The approach requires the definition of (i) a sequence of distribution functions of the increments of the process, and (ii) a sequence of copula functions representing dependence between each increment of the process and the corresponding level of the process before the increment. The paper shows how to use the approach to build several kinds of processes (stable, elliptical, Farlie-Gumbel-Morgenstern, Archimedean and martingale processes), and how to extend the analysis to the multivariate setting. The technique turns out to be well suited to provide a discrete time representation of the dynamics of innovations to financial prices under the restrictions imposed by the Efficient Market Hypothesis.

Suggested Citation

  • Cherubini, Umberto & Mulinacci, Sabrina & Romagnoli, Silvia, 2011. "A copula-based model of speculative price dynamics in discrete time," Journal of Multivariate Analysis, Elsevier, vol. 102(6), pages 1047-1063, July.
  • Handle: RePEc:eee:jmvana:v:102:y:2011:i:6:p:1047-1063
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    References listed on IDEAS

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    1. Brendan K. Beare, 2010. "Copulas and Temporal Dependence," Econometrica, Econometric Society, vol. 78(1), pages 395-410, January.
    2. Ibragimov, Rustam, 2009. "Copula-Based Characterizations For Higher Order Markov Processes," Econometric Theory, Cambridge University Press, vol. 25(03), pages 819-846, June.
    3. repec:sae:ecolab:v:16:y:2006:i:2:p:1-2 is not listed on IDEAS
    4. Paul A. Samuelson, 1973. "Proof That Properly Discounted Present Values of Assets Vibrate Randomly," Bell Journal of Economics, The RAND Corporation, vol. 4(2), pages 369-374, Autumn.
    5. Nikolay Nenovsky & S. Statev, 2006. "Introduction," Post-Print halshs-00260898, HAL.
    6. Florens, J.P. & Mouchart, M. & Rolin, J.M., 1993. "Noncausality and Marginalization of Markov Processes," Econometric Theory, Cambridge University Press, vol. 9(02), pages 241-262, April.
    7. Fama, Eugene F, 1970. "Efficient Capital Markets: A Review of Theory and Empirical Work," Journal of Finance, American Finance Association, vol. 25(2), pages 383-417, May.
    8. Florens, Jean-Pierre & Fougere, Denis, 1996. "Noncausality in Continuous Time," Econometrica, Econometric Society, vol. 64(5), pages 1195-1212, September.
    9. Beare, Brendan K., 2012. "Archimedean Copulas And Temporal Dependence," Econometric Theory, Cambridge University Press, vol. 28(06), pages 1165-1185, December.
    10. Chen, Xiaohong & Fan, Yanqin, 2006. "Estimation of copula-based semiparametric time series models," Journal of Econometrics, Elsevier, vol. 130(2), pages 307-335, February.
    11. Fang, Hong-Bin & Fang, Kai-Tai & Kotz, Samuel, 2002. "The Meta-elliptical Distributions with Given Marginals," Journal of Multivariate Analysis, Elsevier, vol. 82(1), pages 1-16, July.
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    Cited by:

    1. Harb, Etienne & Louhichi, Wael, 2017. "Pricing CDS spreads with Credit Valuation Adjustment using a mixture copula," Research in International Business and Finance, Elsevier, vol. 39(PB), pages 963-975.
    2. Overbeck Ludger & Schmidt Wolfgang M., 2015. "Multivariate Markov Families of Copulas," Dependence Modeling, De Gruyter Open, vol. 3(1), pages 1-13, October.
    3. Cossette, Hélène & Côté, Marie-Pier & Marceau, Etienne & Moutanabbir, Khouzeima, 2013. "Multivariate distribution defined with Farlie–Gumbel–Morgenstern copula and mixed Erlang marginals: Aggregation and capital allocation," Insurance: Mathematics and Economics, Elsevier, vol. 52(3), pages 560-572.

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