Dynamics of the term structure on interest rates: a two-factor model

The main goal of this paper is to develop a model of the term structure of interest rates, based on a Black-Sholes type of arbitrage and study its properties. In order to achieve this objective two state variables are considered: the long-term interest rate l(t), and the spread (difference between the instantaneous and the long-term interest rat), s(t). These two state variables have been previously considered by other researchers: Shaefer and Schwartz (1984) and Moreno (1997). The main differences of this paper from Schaefer and Schwartz's consist on defining l(t) as the long-term interest rate (Schaefer and Schwartz used the consol rate). As a result, the market price of risk associated to this variable is an exogenous parameter of the model. In comparison to Moreno's in this paper the long-term interest rate follows a square root process which does not allow negative rates and the volatility is sensitive to the variations of the process.