We study a class of backtests for forecast distributions in which the test statistic is a spectral transformation that weights exceedance events by a function of the modeled probability level. The choice of the kernel function makes explicit the user's priorities for model performance. The class...

This paper documents a significantly stronger relationship between the slope of the yield curve and future excess bond returns on Treasuries from 2008-2015 than before 2008. This new predictability result is not matched by the standard shadow rate model with Gaussian factor dynamics, but...

Under the revised market risk framework of the Basel Committee on Banking Supervision, the model validation regime for internal models now requires that models capture the tail risk in profit-and-loss (P&L) distributions at the trading desk level. We develop multi-desk backtests, which...