Short-rate diffusion hedging
= Short-rate diffusion hedging
In a <one-factor short-rate model>, a derivative $V(t,r)$ can be hedged locally by a nondegenerate traded <zero-coupon bond> $P(t,r;T_1)$. Match Brownian exposures by holding $V_r/P_r$ bonds and putting the remaining value into the <bank account>. Substitution into the two pricing equations proves the gain identity. This requires $\eta P_r\ne0$; completeness at a degenerate boundary cannot be inferred from the dimension count alone.