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Return and Value at Risk using the Dirichlet Process

Author

Listed:
  • Mahmoud Zarepour
  • Thierry Bedard
  • Andre Dabrowski

Abstract

There exists a wide variety of models for return, and the chosen model determines the tool required to calculate the value at risk (VaR). This paper introduces an alternative methodology to model-based simulation by using a Monte Carlo simulation of the Dirichlet process. The model is constructed in a Bayesian framework, using properties initially described by Ferguson. A notable advantage of this model is that, on average, the random draws are sampled from a mixed distribution that consists of a prior guess by an expert and the empirical process based on a random sample of historical asset returns. The method is relatively automatic and similar to machine learning tools, e.g. the estimate is updated as new data arrive.

Suggested Citation

  • Mahmoud Zarepour & Thierry Bedard & Andre Dabrowski, 2008. "Return and Value at Risk using the Dirichlet Process," Applied Mathematical Finance, Taylor & Francis Journals, vol. 15(3), pages 205-218.
    • Handle: RePEc:taf:apmtfi:v:15:y:2008:i:3:p:205-218
    DOI: 10.1080/13504860701718448
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    References listed on IDEAS

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    1. Dilip B. Madan & Peter P. Carr & Eric C. Chang, 1998. "The Variance Gamma Process and Option Pricing," Review of Finance, European Finance Association, vol. 2(1), pages 79-105.
    2. Zarepour, M. & Knight, K., 1999. "Bootstrapping point processes with some applications," Stochastic Processes and their Applications, Elsevier, vol. 84(1), pages 81-90, November.
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    Cited by:

    1. Zarepour, Mahmoud & Labadi, Luai Al, 2012. "On a rapid simulation of the Dirichlet process," Statistics & Probability Letters, Elsevier, vol. 82(5), pages 916-924.
    2. Han, Yufeng, 2012. "State uncertainty in stock markets: How big is the impact on the cost of equity?," Journal of Banking & Finance, Elsevier, vol. 36(9), pages 2575-2592.

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