This paper develops a model for estimating
Value-at-Risk (VaR) from the historical return series. The proposed method uses
spline interpolation to represent the empirical probability distribution of the
return series. The approach developed in this paper is easy to implement using
available programming platforms, and it can be generalized to other
applications that involve estimating empirical distribution. In order to check
the validity of the model, we use established back-testing methods and show
that the model is robust to the changes in sample size and significance levels
used to estimate VaR. We test the model against some similar distribution-based
models using historical data from S&P500 index. We show that Value-at-Risk
estimation based on the proposed method can outperform common historical,
parametric, and kernel-based methods. As a result, the method can be useful in
the context of validation of market risk models.
JEL classification numbers: C52, C63, G17, G32.
Keywords: Value-at-Risk, Non-parametric
estimation, Empirical distribution, Spline Interpolation.