Implied savings accounts are unique

Abstract

Abstract. An implied savings account for a given term structure model is a strictly positive predictable process A of finite variation such that zero coupon bond prices are given by $B(t,T)=E^Q\left[{A_t \over A_T} \Big| {\cal F}_t \right]$ for some Q equivalent to the original probability measure. We prove that if $(A^\prime,Q^\prime)$ is another pair with the same properties, then A and $A^\prime$ are indistinguishable. This extends a result given by Musiela and Rutkowski (1997a) who considered the case of a Brownian filtration, and fills a gap in their arguments.