Dodgson-Kainth Model

Abstract

In this section we provide some more detail on the derivation of the stochastic inflation-indexed bond price in the Dodgson-Kainth model under the LGM measure:

$${{P}_{I}}\left( {t,T} \right)=\frac{{N\left( t \right)}}{{I\left( t \right)}}\mathbb{E}_{t}^{N}\left[ {\frac{{I\left( T \right)}}{{N\left( T \right)}}} \right]=N\left( t \right)\mathbb{E}_{t}^{N}\left[ {\frac{1}{{N\left( T \right)}}{{e}^{{\int\nolimits_{t}^{T} {i\left( s \right)ds} }}}} \right].$$

(13.20’)