A Non-parametric Method for Calculating Conditional Stressed Value at Risk

Abstract

We consider the Value at Risk (VaR) of a portfolio under stressed conditions. In practice, the stressed VaR (sVaR) is commonly calculated using the data set that includes the stressed period. It tells us how much the risk amount increases if we use the stressed data set. In this paper, we consider the VaR under stress scenarios. Technically, this can be done by deriving the distribution of profit or loss conditioned on the value of risk factors. We use two methods; the one that uses the linear model and the one that uses the Hermite expansion discussed by Marumo and Wolff (2013, 2016). Numerical examples shows that the method using the Hermite expansion is capable of capturing the non-linear effects such as correlation collapse and volatility clustering, which are often observed in the markets.