The term structure of interest rates: the case of imperfect information

The authors consider the problem of valuation of bonds in a market with an imperfectly observable state variable. A natural way to transform the problem of valuation of bonds in an imperfect information market into an equivalent perfect information problem is to assume that bond prices are functionals of the density of the conditional probability distribution of the imperfectly observable state variable. Given that, the authors obtain a valuation equation for bonds through nonlinear filtering methods combined with standard arbitrage arguments. The authors show how the problem of valuation can be drastically simplified if it is considered in the equivalent risk neutral market. For a linear version of the model, the equivalent risk neutral market is used to obtain a closed for solution for bond prices. This version is used to emphasize the effect of the market risk exposure caused by the lack of information on the shape of the yield curve