Return and Value at Risk using the Dirichlet Process

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

Acknowledgement

This paper is dedicated to Andre Dabrowski, who passed away on 7 October, 2006 after a brief but courageous battle with cancer. Dr Dabrowski received his PhD from the University of Illinois in 1982 and joined the faculty at the University of Ottawa in 1985, where he was the Dean of Science at the time of his death. The authors are greatly indebted to two anonymous referees and the co‐editor for several helpful comments. This research is supported by the Natural Sciences and Engineering Research Council of Canada.