The prices of fixed income assets depend on three components (Litterman and Iben ): the risk free term structure of interest rates, embedded options values and credit risk. Optimally allocating portfolios in fixed income markets demands a detailed analysis of each of these components.
Several authors have already considered the risk free term structure estimation problem. For example, Vasicek and Fong  suggest a statistical model based on exponential splines. Litterman and Scheinkman  verified that there are three orthogonal factors which explain the majority of the movements of the US term structure of interest rates. These three factors form the basis for many fixed income pricing and hedging applications. For instance, these factors are used in Singh  to suggest optimal hedges.
Some bonds present embedded options. In general, the price of an embedded option is a nonlinear function of its underlying bond price on all dates before the option maturity date. An embedded option depends not only on the actual term structure of interest rates, but also on the evolution of this term structure during the life of the option. Several models have been proposed for the evolution of the term structure of interest rates. These models are classified in two major groups (Heath et al. ): equilibrium models (Cox et al. , among others) and arbitrage free models (Heath et al. , Ho and Lee , Vasicek , among others).
At this point in time, the pricing of embedded options using arbitrage free models is perceived as the most appropriate because the parameters can be chosen to be consistent with the actual term structure of interest rates and, consequently, to the actual prices of bonds (Heath et al. ). The process modeled can be the shortterm interest rate, the whole term structure of interest rates, or the forward rates curve. No matter what the process is, when it is Markovian, it is usually implemented using binomial trees (Black et al. ) or trinomial trees (Hull and White ).