Computation and Estimation of Shadow Interest Rate Models

Second order cumulant approximation method proposed by Priebsch (2013) is widely used in shadow rate term structure models. We provide an error analysis for this method, demonstrate large potential errors with realistic... [ view full abstract ]

Second order cumulant approximation method proposed by Priebsch (2013) is widely used in shadow rate term structure models. We provide an error analysis for this method, demonstrate large potential errors with realistic parameter configurations, and derive third and fourth order cumulant approximations as the remedy. We show that T-maturity shadow rate volatility (TMSRV) largely determines approximation errors, and thus propose a robust variable order scheme that varies approximation orders based on TMSRV. With estimation on US Treasury data including up to 30-year bonds, we show the second order scheme can generate large errors, while our variable order scheme ensures accuracy.