Un modèle d'équilibre général avec volatilité stochastique des taux d'intérêt et information incomplète

In a general equilibrium framework, we suppose that the variables which characterise the state of the economy are not observable. Agents solve their optimisation problem by first estimating the unobserved state variables given the information carried by the observations. Tools of filtering theory are used to derive optimal estimates. It is shown that, even if the information structure is gaussian, the conditional distribution of the state variables is characterised by two sufficient statistics: the conditional mean and the conditional variance. Then, the control problem is based on the sufficient statistics. It follows that discount bond values and the interest rate diffusion process are functions of the sufficient statistics. In that case, we demonstrate that interest rate volatility is stochastic.