Abstract

Value at Risk (VaR) has become the standard measure of market risk employed by financial industry for both internal and regulatory purposes. VaR is defined as the value that a portfolio will lose with a given probability, over a certain time horizon (usually one or ten days). Despite its conceptual simplicity, its measurement is still a very challenging statistical problem and none of the methodologies developed so far give satisfactory solutions. In this paper, we develop a new approach by expanding the realistic return distribution as linear summation of the standard normal distribution function with its coefficients as Legendre polynomial series to improve the calculation of VaR.  One can obtain the distribution function toward the realistic distribution in any assumed precision. This approach outcomes the usual VaR calculation by assuming the normal distributions.

Finally, we test our approach through a real world data. It is found that our approach give more accurate results for the VaR and also more accurate distribution function than the usual normal distributions.

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