A colleague and I are looking to apply a standard delta/gamma approximation for interest rate derivatives, to obtain of potential values. To simulate the underlying shocks, we are using Hull White short rate model. In deriving the equation (attached), it is apparent that Gamma in fact depends only on the process volatility and time step, but not on the magnitude of the simulated shocks (i.e. the effect of Gamma is deterministic). Hence if we obtain a distribution of potential values using only Delta - the effect of Gamma will be simply to shift the mean, and not change the shape of the distribution.Although this is a natural result of the expansion, it appears somewhat counter-intuitive. Surely the larger the shock, the larger the Gamma effect? What are we missing?