Return and Value at Risk using the Dirichlet Process

Mahmoud Zarepour, Thierry Bedard and Andre Dabrowski

Applied Mathematical Finance, 2008, vol. 15, issue 3, 205-218

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.

Keywords: Dirichlet process; quantiles; Bayes estimates; value at risk (search for similar items in EconPapers)
Date: 2008
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Citations: View citations in EconPapers (2)

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DOI: 10.1080/13504860701718448

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