New Approach to Density Estimation and Application to Value-at-Risk

Abstract

The key contribution in this paper is to provide a new approach in estimating the physical distribution of the underlying asset return by using a quadratic Radon-Nikodym derivative function. The latter function transforms a fitted Variance Gamma risk-neutral distribution that is obtained from traded option prices. The generality of the VG distribution helps to avoid unnecessary mis-specification bias. The estimated empirical distribution is then used to find the risk measure of VaR. We show that possible underestimation of VaR risk using existing methods is largely not due to VaR itself but perhaps due to mis-specification errors which we minimize in our approach. Our method of measuring VaR clearly captures large tail risk in the empirical examples on S&P 500 index.