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Market symmetry in time-changed Brownian models

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  • Fajardo, José
  • Mordecki, Ernesto

Abstract

In this paper we examine which Brownian subordination with drift exhibits the symmetry property introduced by Fajardo and Mordecki [2006. Quantitative Finance 6, 219-227]. We find that when the subordination results in a Lévy process, a necessary and sufficient condition for the symmetry to hold is that the drift must be equal to-1/2. Also, we derive explicit conditions to test whether the NIG, CGMY and Meixner processes are symmetric or not. Finally, we perform some tests with real financial data.

Suggested Citation

  • Fajardo, José & Mordecki, Ernesto, 2010. "Market symmetry in time-changed Brownian models," Finance Research Letters, Elsevier, vol. 7(1), pages 53-59, March.
  • Handle: RePEc:eee:finlet:v:7:y:2010:i:1:p:53-59
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    References listed on IDEAS

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    1. Fajardo, José & Farias, Aquiles, 2009. "Multivariate affine generalized hyperbolic distributions: An empirical investigation," International Review of Financial Analysis, Elsevier, vol. 18(4), pages 174-184, September.
    2. Tehranchi, Michael R., 2009. "Symmetric martingales and symmetric smiles," Stochastic Processes and their Applications, Elsevier, vol. 119(10), pages 3785-3797, October.
    3. José Fajardo & Ernesto Mordecki, 2005. "Duality and Derivative Pricing with Time-Changed Lévy Processes," IBMEC RJ Economics Discussion Papers 2005-12, Economics Research Group, IBMEC Business School - Rio de Janeiro.
    4. JosE Fajardo & Ernesto Mordecki, 2006. "Symmetry and duality in Levy markets," Quantitative Finance, Taylor & Francis Journals, vol. 6(3), pages 219-227.
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    Cited by:

    1. Thorsten Rheinlander & Michael Schmutz, 2012. "Quasi self-dual exponential L\'evy processes," Papers 1201.5132, arXiv.org.
    2. Jos� Fajardo & Ernesto Mordecki, 2014. "Skewness premium with L�vy processes," Quantitative Finance, Taylor & Francis Journals, vol. 14(9), pages 1619-1626, September.
    3. Fajardo, José, 2015. "Barrier style contracts under Lévy processes: An alternative approach," Journal of Banking & Finance, Elsevier, vol. 53(C), pages 179-187.
    4. Thorsten Rheinlander & Michael Schmutz, 2012. "Self-dual continuous processes," Papers 1201.6516, arXiv.org.
    5. José Fajardo, 2014. "Symmetry and Bates’ rule in Ornstein–Uhlenbeck stochastic volatility models," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 37(2), pages 319-327, October.
    6. Rheinländer, Thorsten & Schmutz, Michael, 2013. "Self-dual continuous processes," Stochastic Processes and their Applications, Elsevier, vol. 123(5), pages 1765-1779.

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