Value-at-Risk Estimation Using an Interpolated Distribution of Financial Returns Series

Abstract

Abstract 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.