Implied Correlation from VaR

Most of the methods used by financial institutions to implement value-at-risk models are based on the multivariate Gaussian distribution with a constant correlation matrix. In this paper we use VaR calculation in a reverse way to imply the correlation between asset price changes. The distribution of implied correlation under normality is also studied in order to take into account any bias and sampling error. Empirical results for US and UK equity markets show that implied correlation is not constant but tends to be higher for long positions than for short positions. This result is statistically significant and can be interpreted as departure from normality. Our test provides a new way - by focusing the tail dependence - to assess the model risk associated with quantitative methods based on normality in asset management and risk management areas.

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