The goal of this code is to automatically create a "Risk Map" from a series of Value-at-Risk (VaR) and profit and loss (P&L). Given the time series of VaR(α) and P&L, we generate the corresponding time series for VaR(α'), with α'<α through calibration. This is done by extracting the conditional variance of the P&L from VaR(α) and then plugging it into the formula for VaR(α'). A "super exception" is then defined as P&L < -VaR(α'). We formally test whether the sequence of exceptions and super exceptions satisfies standard backtesting conditions. Finally, the Risk Map graphically summarizes all information about the performance of the risk model.
Journal of Monetary Economics (2018)
Toda Alexis Akira