ABSTRACT
This chapter explores the stochastic evolution for the zero-coupon bond price curve. The stochastic structure is introduced sequentially, starting with a one-factor model, then presenting a two-factor model, and so forth. Starting with the simplest stochastic structure facilitates understanding. After this one-factor model is mastered, additional factors can be added in a straightforward fashion. The state space process describes the uncertainty underlying and generating the evolution of all the zero-coupon bond prices. The evolution of the zero-coupon bond prices, in turn, determines the evolution of the forward rates and the spot rates. The stochastic process for the spot rate can be deduced from the zero-coupon bond price process’s evolution. The entire zero-coupon bond curve is pairwise linked to adjacent maturity zero-coupon bonds. Consequently, to be consistent with an economic equilibrium, there must be some additional explicit structure required on the parameters of the evolution of the zero-coupon bond price curve.
